SCALES 1st General Meeting - Superfluid Condensates in Astrophysics and Laboratory Experiments

Jun 22, 2026, 8:00 AM → Jun 26, 2026, 6:10 PM Europe/Lisbon

Physics Department, University of Coimbra

Warning: The organisers have not asked any agency or travel company to arrange for accommodation, so please ignore any emails regarding hotel bookings for the conference. Please be aware of this and consider them spam.

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Deadline for payments: June 7

Schedule now online!

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New information in sections "Travel to Coimbra", Where to Eat" and "Social Program"!

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Superfluidity is a striking phenomenon observed in many quantum fluids, which can flow without viscosity when cooled to low temperatures. Recent experimental advances allow us to study and visualise the complex flows of these systems in the presence of vorticity, and track the dynamics of quantum vortices far from equilibrium, both for bosonic and fermionic superfluids. Experiments with helium-4 and helium-3 allow the analysis of quantum turbulence on different scales, while cold atomic gases allow exquisite studies of single vortex dynamics in a variety of regimes, spanning the entire crossover from molecular Bose-Einstein condensates (BEC) to Bardeen-Cooper-Schrieffer (BCS) superfluids. Moreover, a growing body of theoretical and observational evidence suggests that nucleons in neutron stars are paired and form a fermionic superfluid, the dynamics of which is thought to be at the origin of the observed radio pulsar glitches.

The next years will bring a wealth of data on neutron star dynamics, from new radio observatories such as the Square Kilometer Array (SKA), but especially from gravitational wave observations with next-generation detectors, like the planned European Einstein Telescope (ET). Direct laboratory analogues of superfluid neutron stars are now being studied with superfluids on rotating platforms, but this connection is neither systematically explored nor disseminated among the relevant scientific communities.

The COST Action SCALES (https://camk.pl/SCALES/index.html) will bring together novel laboratory experiments, emerging massive parallel simulations, and neutron star experts to kickstart this new avenue of superfluidity research and pave the way for new discoveries across different scales. 

The first Action wide meeting will  include plenary sessions describing the physical problems at the basis of each working group (WG), and the objectives of the different WGs will be present (specifically open problems in Cold Atoms, Helium and Neutron Star superfluidity), as well as submitted abstracts. Submission by young researchers is encouraged, as well as multi-disciplinary talks that create convergence between WGs. The choice of participants to be reimbursed by the Action will be made against a set of MC approved criteria, that include COST policy criteria, and additional items (regarding relevance to action objectives).

INVITED SPEAKERS: 

-Andrei Igoshev, Newcastle University, UK

-Arus Harutyunyan, Byurakan Astrophysical Observatory, Armenia

-Bugra Tuzemen, Institute of Physics of the Polish Academy of Sciences, Poland

-Clara Dehman, University of Alicante, Spain

-Dario Ballarini, CNR Nanotech, Italy

-Elena Poli, University of Trento, Italy

-Eric Dong, University of Melbourne, Australia

-Gary Liu, Royal Holloway University of London, UK

-Klejdja Xhani, Politecnico di Torino, Italy

-Mihailo Cubrovic, Institute of Physics Belgrade, Serbia

-Nils Andersson, University of Southampton, UK

-Rena Zieve, University of California, Davis, USA

-Riku Rantanen, Aalto University, Finland

-Saso Grozdanov,  University of Ljubljana, Slovenia

-Thomas Gasenzer, University of Heidelberg, Germany

-Tuhin Malik, University of Coimbra, Portugal

SCIENTIFIC ORGANIZING COMMITTEE:

-Bryn Haskell 

-Vanessa Graber 

-Daniel Pecak

-Giulia del Pace

-Emil Varga

-Luca Galantucci

-Nicolas Chamel

-Danai Antonopoulou

-Melissa Mendes

-Andrea Richaud

-Marco Antonelli

-Helena Pais

-Hugo Terças

LOCAL ORGANIZING COMMITTEE:

-Helena Pais (UC)

-Hugo Terças (ISEL)

-Constança Providência (UC)

-Tuhin Malik (UC)

-Tiago Custódio (UC)

-Milena Albino (UC)

-Rafael Cardoso (UC)

-Isabel Melo (Secretariat - ADDF)

 

IMPORTANT INFORMATION /DATES:

-March 11: Registration opens

-March 11: Abstract submission opens

-May 15: Abstract submission closes

-May 15: Deadline to request financial support

-May 30: Notification of abstract acceptance

-May 30: Notification of financial support

-June 1: Registration closes

-June 5: Program released

-June 7: Deadline for payments

 

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Mon, June 22

Registration

Opening

WG1 - Vortex Dynamics: 1st morning session

Convener: Brynmor Haskell (Universita' degli Studi di Milano, Italy)

1 Vortices and glitches in rotating dipolar supersolids

Since the realization of the first dipolar Bose–Einstein condensate (BEC) of strongly magnetic atoms, long-range and anisotropic dipole–dipole interactions have enabled the emergence of novel quantum phases driven by interaction-induced density modulations. Among these, the most remarkable is the supersolid phase, which simultaneously combines crystalline order with global phase coherence. In particular, the recent achievement of two-dimensional supersolidity has opened a new avenue for exploring the system’s rotational response. In this talk, I will present the most recent theoretical and experimental results on vortex nucleation in two-dimensional supersolids and the subsequent rich and intriguing vortex-crystal dynamics. Finally, I will show an application of rotating dipolar supersolids, i.e. the possibility to simulate “glitches”, instantaneous jumps of the rotation frequency occurring due to the internal vortex dynamics, akin to observations in neutron stars.

Speaker: Elena Poli (Pitaevskii BEC Center, CNR-INO, Trento, Italy)

2 Modelling Vortex Avalanches in Neutron Stars using the Vortex Filament Model

Neutron stars are the collapsed cores of massive stars that have undergone a supernova explosion. They are the densest known astrophysical objects, with a mass typically 1.4 times that of the Sun compressed into a radius of approximately 10 km. Deep within the star, where the density exceeds the nuclear equilibrium density, neutrons become superfluid and protons become superconducting. As a result, the star’s rotation and magnetic flux become are quantised into extremely thin vortices and fluxtubes respectively. These vortices pin to nuclear lattice sites or defects in the star’s crust. When the star’s rotation rate slows down, the vortices move outward to conserve angular momentum. At the same time, these vortices unpin and self-reorganise to release the stored angular momentum in catastrophic discrete events known as rotational glitches which are observed as an instantaneous increase in the observed rotation rate of pulsars. A complete theory of the micro and macroscale superfluid dynamics to explain this phenomenon does not yet exist and current theoretical models are hampered by an incomplete understanding of the interactions between superfluid vortices, fluxtubes and crustal nuclei. In my talk, I would like to focus on the latest results of modelling vortex avalanches using mesoscopic models of superfluidity, namely the point vortex model and the vortex filament model. In particular, I will show the latest results of our attempts to simulate vortex avalanches using a relatively large vortex lattice in the vortex filament model, which is a regime that has not been fully explored before.

Speaker: Julie Jacob Thomas (Newcastle University)

3 Vortex Pinning, 2D Turbulence, and Vorticity Avalanches in Nanoconfined Helium-4

I will present work that investigates the dynamics of quantized vortices in superfluid $^4$He confined to nanoscale geometries, where vortex motion is strongly influenced by pinning on disordered substrate surfaces. We present a numerical model for quasi-2D geometries that captures vortex-surface interactions as a velocity-dependent mutual friction; results from our numerical simulations show good agreement with experimental observations of decaying 2D turbulence in 500 nm vertical confinement. To further probe these dynamics, we introduce a high-sensitivity electromechanical setup—a nanofluidic Helmholtz resonator parametrically coupled to an RF LC circuit. By leveraging dynamical backaction to enhance the dissipation sensitivity of fourth-sound modes, we achieve vortex detection in 900 nm channels at relatively short timescales allowing the study of the vortex dynamics. Experimental studies of vortex states created by external rotation reveal evidence of vorticity avalanches and a significant dependence on system history, providing new insights into the complex interplay between vortex pinning and fluid flow in confined superfluids.

Speaker: Emil Varga (Univerzita Karlova, Faculty of Mathematics and Physics)

10:40 AM Coffe Break

2nd morning session

Convener: Elena Poli (Pitaevskii BEC Center, CNR-INO, Trento, Italy)

4 Structure and Dynamics of Pairing Field in Inhomogeneous Fermi Superfluids

Spin imbalance in ultracold Fermi gases gives rise to a rich variety of structures rooted in the competition between pairing and polarization. I will present a survey of our recent results, starting from the static phase diagram where disordered configurations compete energetically with Larkin-Ovchinnikov-Fulde-Ferrell (LOFF)-type ordered states across a wide range of polarizations. I will then turn to dynamics, where quantum vortices emerge as sensitive probes of the underlying superfluid structure. Topics include vortex dipole deflection by localized spin-polarized regions, vortex-mediated spin transfer in disk geometries, and the distinct regimes that appear in spin-imbalanced ring systems, from polarized vortex cores to LOFF-like persistent current states.

Speaker: Bugra Tuzemen (IFPAN)

5 Bouquets of Topological Defects and Pinning in Neutron Stars

Quantised vortices and magnetic flux tubes are expected to govern key aspects of neutron star dynamics, but their bulk behaviour is difficult to isolate numerically due to boundary effects in finite domains. Despite an unavoidable topological obstruction, it is possible to study topological defects in periodic domains by relaxing the requirement of periodicity for the condensate's phase. Building on this idea, I will present a Gross-Pitaevskii framework with quasi-periodic boundary conditions for vortex dynamics at finite net vorticity (and its related public simulation code, GINTONIC), and a two-component Ginzburg-Landau model for coupled neutron and proton condensates. Together, these models provide a way to study how topological defects interact while avoiding possible spurious effects associated with hard walls or confining potentials. In particular, I will discuss how this framework can be used to investigate type-1.5 superconductivity in neutron stars, the formation of flux-tube bouquets around vortices, and the pinning of vortices to flux tubes.

GitHub code repository: GINTONIC - Gross-Pitaevskii Integrator on a Torus with non-zero Vorticity, https://github.com/Magistrelli/gintonic

Based on: Dynamics of quantized vortices under quasi-periodic boundary conditions, https://arxiv.org/abs/2509.15298

Speaker: Marco ANTONELLI (CNRS - LPC Caen)

6 Reassessing pulsar braking indices: A vortex line–flux tube interaction model

An extended superfluid vortex line–magnetic flux tube interaction model is proposed for the magneto-thermal-rotational evolution of neutron stars. Applications to a sample of 12 radio pulsars with reliably measured braking indices demonstrate significantly improved agreement compared to the preexisting models. The effective moment of inertia change term for glitching pulsars is derived from vortex creep theory and connected to the directly observable glitch activity parameter, making the model fully predictive for the glitching sources as well.
This work paves the way for a fully self-consistent coupled magneto-thermal–rotational evolution model of neutron stars, incorporating the microphysical vortex pinning/creep framework, realistic core magnetic field configurations with various dissipation mechanisims, and modern neutron star cooling codes.

Speaker: erbil gügercinoğlu (Sabancı University)

12:50 PM Lunch

1st afternoon session

Convener: Bugra Tuzemen (IFPAN)

7 Vortex pinning in a spin-triplet superfluid

Vortex dynamics in superfluids is strongly affected by the presence of impurities or obstacles that can act as pinning sites. Pinning of quantized vortices inside a neutron star is predicted to play an important role in its rotational dynamics and can lead to sudden changes in angular velocity known as glitches. In a system with a multicomponent order parameter, such as a spin-triplet superfluid expected to form in the core of a neutron star, the interaction between vortices and pinning sites can be more complicated due to the non-trivial structure of the vortex cores. Superfluid $^3$He is a model example of a spin-triplet system where a wide variety of different types of vortices have been observed [1,2], and where pinning sites can be introduced in experiments via nanoscale confinement [3].

We study the structure of vortex cores in superfluid $^3$He using the Ginzburg-Landau formalism, and the problem of a vortex pinned by columnar defects with sizes comparable to the coherence length. We calculate both the depinning velocity and the shape of the energy barrier for the depinning process. The multicomponent nature of the order parameter can lead to fractional depinning, where the vortex detaches from the defect as two half-quantum vortices.

[1] R. Rantanen and V. B. Eltsov, PRR 6, 043112 (2024)
[2] S. Autti et al., PRL 117, 255301 (2016)
[3] S. Autti et al., PRR 2, 033013 (2020)

Speaker: Riku Rantanen (Aalto University)

8 Investigating pinning in neutron stars with simulations and laboratory experiments

Vortex pinning in neutron stars: i.e. strong interactions between superfluid neutron vortices and normal components of the star, is a key ingredient in theoretical models for astrophysical phenomena such as pulsar glitches.
In this talk I will describe how we can make progress in understanding the nature of pinning by studying a laboratory analogue system, i.e. superfluid Helium 3 in the presence of pinning to different kinds of aerogel.
I will discuss the results that can be obtained from the results of experiments in such systems, and also briefly describe simulations of vortex motion in neutron star crusts, that allow to extrapolate the results to conditions that cannot be studied in terrestrial systems.

Speaker: Brynmor Haskell (Universita' degli Studi di Milano, Italy)

9 Vortex Avalanches and Pinning Scales

Vortex avalanches as distinct from large fluctuations in continuous dynamics require the breaking of scale invariance. A simple model for avalanches, based on intrinsic scales of pinning forces and of substrates sustaining pinning centers is presented. Applications to pulsar glitches and analogue experiments in laboratory condensates are discussed.

Speaker: Ali Alpar (Sabanci University)

4:10 PM Coffee Break

2nd afternoon session

Convener: Riku Rantanen (Aalto University)

10 Local Quantum Cooling for Large Fermi Systems with Pairing

We present a framework for local quantum cooling that can be efficiently applied to large-scale Fermi systems. The method introduces local Hermitian operators as a cooling potential while strictly preserving the unitarity of time evolution. Our formulation scales favorably with system size and can be seamlessly integrated into time-dependent density functional theory frameworks. We demonstrate that energy cooling arises from the damping of particle currents and pairing-field fluctuations. Furthermore, we develop a variant of the scheme that allows the particle number to vary in time, enabling controlled density scans. The method is generic and versatile, as illustrated by applications to spin-imbalanced unitary Fermi gases and to nuclear matter in the neutron-star crust. The framework can be naturally extended to include stochastic noise, providing a foundation for studying thermalization in strongly interacting Fermi superfluids.

Speaker: José Ernesto Alba-Arroyo (Warsaw University of Technology)

11 Josephson effects and atomtronic circuits in atomic superfluids

Josephson junctions provide a fundamental platform to study the interplay between macroscopic phase coherence and dissipation, with relevance ranging from quantum technologies and superconductors to neutron stars. Ultracold atomic gases, with tunable interactions and controllable geometries, enable exploration of Josephson dynamics across the BEC–BCS crossover within a single system.

We investigate the dynamical regimes of atomic Josephson junctions in both simply[1-5] and multiply connected [6] geometries. Below a critical velocity, coherent Josephson oscillations occur; above it, dissipation sets in through mechanisms that depend on the interaction regime and temperature. In simply connected elongated 3D systems, dissipation is governed by vortex rings and sound emission on the BEC side [1-2], and by pair breaking in the BCS regime [3], with additional thermal damping at finite temperature [4-5]. Increasing the barrier strength suppresses vortex motion[1-2] and can induce macroscopic quantum self-trapping [2].

In multiply connected (ring) geometries, the system supports quantized persistent currents. Here, dissipation due to vortex emission can be controlled by increasing the number of Josephson junctions. This motivates atomtronic Josephson “necklaces,” ring-shaped superfluids with multiple tunneling links. We study finite-circulation states and show that adding junctions enhances the maximum sustainable circulation (critical current), as the quantization of the circulation in this geometry distributes the total phase across links, reducing the phase drop and superfluid velocity at each junction. This increased stability contrasts with the decreasing superfluid fraction predicted by Leggett’s criterion. Our results are supported by experiments in both elongated (single-junction) [1] and annular geometries with up to 16 junctions [6].

References:
[1] K. Xhani et al., Physical Review Letters 124, 045301 (2020).
[2] K. Xhani et al., New Journal of Physics 22 (2020) 123006.
[3] G. Wlazłowski, K. Xhani et al., Physical Review Letters 130, 023003 (2023).
[4] K. Xhani et al., Phys. Rev. Research 4, 033205 (2022).
[5] K. Xhani et al., Atoms 2025, 13(8), 68 (2025);
[6] L. Pezzè, K. Xhani, C. Daix* et al., Nature Communications 15, 4831 (2024).

Speaker: Klejdja Xhani (Politecnico di Torino, Department of Applied Science and Technology)

Welcome Reception

Tue, June 23

WG2: Superfluid Turbulence: 1st morning session

Convener: Klejdja Xhani (Politecnico di Torino)

12 Glitch Studies in Superfluid Helium

My lab has begun a superfluid helium experiment designed to exhibit glitch behavior, modeled after the Tsakadze and Tsakadze experiment from the 1970's. We levitate a bucket of helium, rotate the bucket, and let the bucket slow down while monitoring its angular velocity. We do observe glitches in which the angular velocity increases. I will discuss various effects that currently limit the precision and time resolution of our measurements. A planned redesign of the experiment should eliminate several of these issues. It should also make the experiment cheaper and more practical for acquiring large amounts of data.

Speaker: Rena Zieve (University of California, Davis)

13 BEC phase transitions in a system of interacting relativistic bosonic particles and antiparticles at finite temperatures

The thermodynamic properties of a system of interacting relativistic bosonic particles and antiparticles at high temperatures and densities, in the presence of the Bose-Einstein condensate, are studied. The density functional mean-field model and the scalar field model were used to calculate phase diagrams and thermodynamic quantities for different ratios of attractive to repulsive forces in the system. As an example, a system of interacting pions ($\pi^{\pm}$) was considered. It is shown that, depending on the interaction constant, four types of phase transitions to the condensate phase exist in such a system. Three are second-order phase transitions, and one is a first-order phase transition. Model calculations were compared with up-to-date lattice data, and parameters were fitted accordingly.

Speaker: Dr Denys Zhuravel (Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine)

14 Reproducible nucleation and control of stable quantum vortex rings in Bose-Einstein condensates

Understanding vortex dynamics in three-dimensional superfluid systems emerges as a key challenge. Driven by the ultracold quantum gases laboratory that has recently been established in Milan, I will present a work [1] aimed at numerically investigating and controlling three-dimensional vortex ring formation and dynamics in trapped Bose-Einstein condensates.
In this work, we propose and numerically validate an experimentally feasible on-demand protocol for the nucleation and manipulation of stable quantum vortex rings in harmonically trapped cylindrical Bose–Einstein condensates. Sweeping a laser-sheet barrier through the condensate, we locally constrict the superflow and trigger vortex-ring formation. By tuning the barrier height and width, and by scanning the barrier velocity, we identify the onset of periodic vortex-ring generation above the critical velocity and achieve direct, deterministic control over the ring nucleation position, radius and hence propagation speed.
Once the ring has formed, we apply tailored local optical potentials to reshape the vortex ring and excite clean Kelvin waves on it, or deliberately induce its destabilisation.
Our results provide a foundation for systematic studies of three-dimensional vortices in atomic superfluids and open the door to tailored vortex dynamics and interactions, enabling controlled access to quantum turbulence.

References:
[1] G. Iori, K. Xhani, W.J. Kwon, D.E. Galli, L. Galantucci, arXiv:2603.09746 (2026)

Speaker: Giorgia Iori (Università degli Studi di Milano)

10:40 AM Coffee Break

2nd morning session

Convener: Rena Zieve (University of California, Davis)

15 Dynamical universality in a driven quantum fluid of light

Universal scaling near phase transitions is one of the central ideas of physics, linking the growth of spatial correlations to the slowing down of dynamics. So far, direct experimental access to this critical behavior has remained largely confined to equilibrium many-body systems, and especially to static critical behavior. Here we probe how universality emerges in a driven quantum fluid of light formed by exciton–polaritons in a semiconductor microcavity. By probing the fluctuation-dominated disordered phase below the condensation threshold, we directly measure both the static growth of the correlation length 𝜉 and the dynamical slowing down of the relaxation time 𝜏.
We find that these quantities obey the universal relation 𝜏 ∝ 𝜉2 where 𝑧 ≈ 2 is the dynamical exponent revealing diffusive dynamics of a non-conserved order parameter. Our results extend the physics of critical dynamics from equilibrium matter to driven optical systems, bridging quantum condensates and lasers.

Speaker: Dario Ballarini (CNR Nanotec)

16 Cold atoms in an optical cavity: from phase transitions to subradiant scattering

Cold atoms trapped in the volume of a high-finesse optical resonator [1] form a hybrid quantum system, where strong atom-light coupling leads to a bistability involving hyperfine ground states [2]. This transition can be exploited both in the preparation and in the detection of atomic quantum states. We experimentally demonstrate an optical bistability between two hyperfine ground states [3]. We interpret the phenomenon in terms of the recent paradigm of first-order, driven-dissipative phase transitions, where the transmitted and driving fields are understood as the order and control parameters. The key point is to quantify and understand fluctuations in the vicinity of the critical point. A unique feature of cavity systems is that the cavity field and its fluctuations can be monitored real time [4], that helps us to reveal the very nature of these phase transitions. Arranging the atoms in an incommensurate lattice with respect to the resonator mode, the scattering into the cavity is suppressed by destructive interference: resulting in a subradiant atomic array. We experimentally demonstrate strong collective coupling of the atoms to the cavity vacuum field by linear scattering from a transverse drive. We show, that strong collective coupling leads to a drastic modification of the excitation spectrum, as evidenced by well-resolved vacuum Rabi splitting in the intensity of the fluctuations [5].

[1] D. Varga, B. Gábor, B. Sárközi, K.V. Adwaith, D. Nagy, A. Dombi, T.W. Clark, F.I.B. Williams, P. Domokos, A. Vukics: Loading atoms from a large magnetic trap to a small intra-cavity optical lattice, Phys. Lett. A 505, 129444 (2024).
[2] B. Gábor, D. Nagy, A. Vukics, P. Domokos: Quantum bistability in the hyperfine ground state of atoms, Phys. Rev. Research 5, L042038 (2023).
[3] B. Gábor, D. Nagy, A. Dombi, T. W. Clark, F. I. B. Williams, K. V. Adwaith, A. Vukics, P. Domokos: Ground-state bistability of cold atoms in a cavity, Phys. Rev. A 107, 023713 (2023).
[4] T. W. Clark, A. Dombi, F. I. B. Williams, Á. Kurkó, J. Fortágh, D. Nagy, A. Vukics, P. Domokos: Time-resolved observation of a dynamical phase transition with atoms in a cavity, Phys. Rev. A, 105, 063712 (2022).
[5] B. Gábor, K. V. Adwaith, D. Varga, B. Sárközi, Á. Kurkó, A. Dombi, T. W. Clark, F. I. B. Williams, D. Nagy, A. Vukics, P. Domokos: Demonstration of strong coupling of a subradiant atom array to a cavity vacuum, EPJ Quantum Technology, 12:93 (2025).

Speaker: David Nagy (HUN-REN Wigner RCP)

17 Kelvin-Helmholtz Instability in Fermionic Superfluids: Numerical Approach

The Kelvin–Helmholtz instability (KHI) in superfluid systems with annular geometry has recently attracted significant attention. While numerical studies based on Gross–Pitaevskii and Zaremba–Nikuni–Griffin models have explained some of its dynamics, the inconsistency persists, as evidenced by incorrect predictions of the instability's growth rates. We employ the SLDA framework to simulate KHI in annular superfluid systems across interaction regimes for temperatures T/Tc ≈ 0.0 and 0.3, and compare the resulting dynamics and KHI growth rates with existing theoretical models and experimental observations. We do not observe sensitivity of the instability growth rate to the interaction regime (BCS vs UFG), in contrast to experimental findings. This discrepancy persists even when finite-temperature effects are included. Additionally, systematic deviations from the Point-Vortex Model are identified for modes with m/Δw ∈ (0.6, 0.8), for which no clear mechanism has been established. In the deep BCS regime, the dynamics change qualitatively: vortex proliferation at the inner edge of the ring dominates, operating on shorter timescales than KHI and suppressing its development. Our results indicate limitations of the SLDA in capturing experimentally observed interaction-dependent growth rates and reveal a competing instability mechanism in the BCS regime. These findings highlight unresolved aspects of vortex dynamics in annular superfluids and motivate further theoretical investigation.

Speaker: Michał Śliwiński (Warsaw University of Technology)

12:50 PM Lunch

1st afternoon session

Convener: Dario Ballarini (CNR Nanotec)

18 Quantum turbulence in a Bose gas close to an anomalous non-thermal fixed point

Our work focuses on decaying quantum turbulence in the vicinity of an anomalous non-thermal fixed point (NTFP) characterized by slow, subdiffusive coarsening of a length scale. The NTFP is approached in the temporal evolution of a quasi-2d dilute Bose gas starting from variously sampled initial vortex configurations. The universal dynamics is accompanied by the build-up of an inverse energy cascade following the Kraichnan-Kolmogorov $k^{-5/3}$ power law in the incompressible energy spectrum. By studying higher moments of the velocity circulation, we observe spatial intermittency when the system is close to the anomalous non-thermal fixed point. Due to the irreversible conversion of incompressible (vortices) into compressible energy (sound) the observed universal dynamics can be understood in the context of decaying, compressible turbulence. The universal characteristics is seen in a similar fashion in systems with contact as well as long-range dipolar interactions. While the spatial characteristics resemble that of classical Kraichnan-Kolmogorov turbulence, the subdiffusive universal temporal scaling exponent $\beta\approx1/5$, which defines the algebraic coarsening of the vortex pattern is found to be distinctly different from results known for classical fluids.

Speaker: Prof. Thomas Gasenzer (Heidelberg University, Germany)

19 Beyond the thousands: Lessons from simulating a neutron star with 10^5 quantized vortices

A neutron star is expected to contain a rotating neutron superfluid, threaded by 10^17 quantized vortices, in an environment with a much larger number of pinning sites. The interaction between these two entities, along with the spin-down of the star's crust, is thought to be the primary driver of pulsar glitches. Given reasonable computational resources, existing Gross-Pitaevskii simulations of this system can handle about 600 vortices. Meanwhile, hydrodynamic simulations can support up to 10^4 point vortices in 2D, but are often constrained by a limited set of pinning strengths. Here, we present a fast and robust simulation suite enabling the tracking of up to 10^5 vortices against a background of pinning sites having a wide range of strengths. We achieve this by adapting the Barnes-Hut algorithm to a well-established hydrodynamic prescription. Utilizing this setup to study the evolution of the pinned vortex array in a spinning-down neutron star, we find that the vortex array does not expand outward uniformly, as often expected. Instead, it spontaneously separates into macroscopic vortex-dense and vortex-scarce regions. This emergence of a geometric length-scale carries immediate relevance for the propagation of pulsar glitches. We conclude by demonstrating the flexibility of our modular suite by establishing a star with significant pinning inhomogeneities, such as those expected to result from crustquakes. We find that the small glitches in this case are staggered and carry an imprint of the underlying inhomogeneity.

Speaker: Anantharaman Viswanathan (Ashoka University)

20 Modeling neutron star glithces triggered by superfluid vortex avalanches

Neutron stars glitches, sudden spin-up events observed in their rotation, can be attributed to a transfer of angular momentum from an internal superfluid reservoir through a superfluid vortex-avalanche process. This research extends existing models by introducing new hypotheses in order to achieve a self-consistent description of superfluid vortex dynamics and avalanche probability. Specifically, the effects of vortex inertial mass were analyzed alongside the introduction of a Gaussian shape for the potential describing the interaction of vortices with pinning centers in the stellar crust. A self-consistent velocity- and position-dependent drag parameter was employed to account for dissipative forces.
Results indicate that, while the introduction of inertial mass has a negligible impact under realistic neutron star crust parameters, the Gaussian reshaping of the potential together with the definition of the drag highly affects the dynamics. A statistical approach based on the evaluation of the vortex mean free path provided a time-dependent description of the vortex-avalanches probability, yielding results aligned with observational data. Despite limitations arising from the point-particle description of the vortex and the assumption of a perfectly periodic crystal lattice in the crust, this model provides a robust framework for future developments aimed at incorporating additional physical ingredients to further increase its generality.

Speaker: Alessandro Costanzo

21 Quantum many-body physics of ultracold Fermi gases on a spherical surface

Recent experimental realizations of ultracold atom bubble traps in microgravity conditions have triggered the exploration of quantum many-body physics in curved geometries, beyond the flat-space paradigm. We investigate a two-component Fermi gas on a spherical surface, analyzing how the interplay between curvature and interactions modifies its physical properties, both at finite and zero temperatures. Starting from the non-interacting case, we derive the finite-temperature Stoner criterion for repulsive interactions to study the stability of the spin-balanced phase. Furthermore, we explore the BCS–BEC crossover as the system evolves from a weakly paired (BCS) regime to a strongly paired (BEC) regime. Across all the investigated regimes, our results reveal the emergence of pronounced shell effects and curvature-induced corrections that significantly deviate from standard two-dimensional flat-space predictions, especially in the low-temperature regime. Remarkably, while differences with respect to flat case results tend to zero in the deep BEC regime, where the dimers have a size much smaller than the sphere, such differences instead are extremely marked in the deep BCS regime. In this limit, the Cooper pair size is bounded by the sphere radius $R$, forcing the system to probe the global curvature of the manifold.

Speaker: Lorenzo Frigato (Università degli Studi di Padova)

22 Performance and Dynamics of an Ultracold Atomic Superfluid as a Quantum Engine Working Fluid

Bose-Einstein condensation is a ubiquitous phenomenon, present across a multitude of physical scales, from coherence among some thousands of atoms, to macroscopic superfluidity in liquid helium, up to theorised superfluid-superconducting neutrons and protons responsible for observed glitches in neutron stars. At all of these scales, questions persist around the subject of non-equilibrium dynamics, turbulence, and dissipation, to which the quantum, non-linear nature of superfluidity introduce mechanisms and features intractable by classical approaches. Remarkably, since the inaugural achievement of Bose-Einstein condensation in an ultracold atomic gas in 1995, atomic superfluids have rapidly developed into a highly controllable and flexible platform to probe ever more diverse and complex superfluid phenomena. One system which was fundamental to the study of equilibrium, non-equilibrium, driven-response and dissipative dynamics of fluids in the development of classical thermodynamics, is the engine. Recently, we have seen atomic superfluid experiments demonstrate the feasibility of constructing an engine system in a real laboratory system. Inspired by the work of Simmons et al in their 2023 paper (PRR 5, L042009 (2023)), in collaboration with experimentalists at Aarhus University we present an investigation of a quantum engine, with a 39K atomic superfluid as the working fluid. We demonstrate efficiency and power performance characteristics subject to variations in compression and interaction strength ratio, as well as finite temperature. We note the rapid convergence of this system to its reversible limit efficiency in finite duration cycles, as well as a novel driving regime which allows simultaneous maximisation of efficiency and power of the cycle.

Speaker: Henry Harper-Gardner (Newcastle University)

23 Interactive 3D Particle-In-Cell Simulation of a Global Pulsar Magnetosphere

We present an interactive 3D Particle-In-Cell (PIC) simulation of a global pulsar magnetosphere implemented in a browser-based HTML/WebGL environment. The model self-consistently evolves electromagnetic fields and relativistic plasma by solving Maxwell’s equations on a discretized grid (Yee scheme) coupled to particle dynamics via the Lorentz force. Charged particles are advanced using a relativistic Boris pusher, while charge and current densities are deposited onto the grid to ensure consistent field–particle coupling.

The simulation captures key physical processes of pulsar magnetospheres, including rotation-induced electric fields, charge separation, current closure, and the formation of equatorial current sheets near the light cylinder. Pair injection is modeled through parameterized source terms to approximate cascade processes in the open-field-line region. A dipolar magnetic field anchored to a rotating neutron star provides the global structure, enabling exploration of aligned and oblique rotator configurations.

Although limited in resolution compared to large-scale HPC PIC codes, the implementation preserves the essential kinetic and electrodynamic behavior reported in the literature. The interactive interface exposes physically meaningful parameters—such as rotation rate, magnetic field strength, obliquity, and pair production rate—allowing users to investigate transitions between vacuum, charge-separated, and quasi force-free regimes. This work aims to provide a scientifically grounded, accessible platform for both education and rapid conceptual exploration in computational astrophysics.

Speaker: Armin Vahdat (University of Tübingen)

24 Probing the Stability of Neutron Star Magnetic Fields through Configurational Entropy

The internal magnetic field configuration of neutron stars remains a key open problem in relativistic astrophysics, with significant implications for their evolution and electromagnetic and gravitational-wave emission. In our work, we investigated the stability of axisymmetric magnetic field configurations in a $n=1$ polytropic neutron star by combining the study of Configurational Entropy (CE), i.e., a measure of informational complexity in Fourier space, with magnetohydrodynamic simulations performed using the PLUTO code. The equilibrium solutions of our model of the magnetic field are described by a discrete set of eigenvalues $\lambda$, which regulate the relative strength and complexity of the toroidal and poloidal components. We found that the CE of the magnetic energy density exhibits a clear maximum at the second eigenvalue, indicating a transition between stable and unstable configurations. Numerical simulations support this interpretation: the lowest eigenvalue configuration, corresponding to minimum energy at fixed magnetic helicity, remains stable over multiple Alfvén timescales, whereas higher-$\lambda$ configurations undergo significant magnetic rearrangement and energy dissipation. These results suggest that configurational entropy provides an effective diagnostic tool for the assessment of stability in magnetised compact objects and place quantitative constraints on the allowed complexity of their internal magnetic field structure.

Speakers: Brynmor Haskell (Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences), Davide Castellani (Università degli Studi di Milano)

4:10 PM Coffee break

2nd afternoon session

Convener: Prof. Thomas Gasenzer (Heidelberg University, Germany)

25 Neutron star glitches in dipolar atoms: towards a layered structure

Pulsars, i.e. fast rotating neutron stars, exhibit an intriguing phenomenon known as “Glitches”. A glitch refers to a sudden increase of the star rotation frequency, which then eventually relaxes back to its slow-down value. The underlying mechanism governing such a behavior is a big open question in the community. A possible explanation is connected to the stochastic unpinning of quantized vortices residing within the stellar interior [1]. In our work, we use a rotating ultracold supersolid as a simulator for the interior of a pulsar. This mechanism has been numerically investigated by slowing down a rotating superfluid in which vortices are pinned by a suitable external potential [2]. Dipolar supersolids, however, provide a more natural and versatile platform for exploring these dynamics. In the supersolid phase, the spontaneous superfluid density modulation naturally provides the forces for vortex trapping, eliminating the need for artificial pinning sites [3]. By spatially tuning the isotropic interaction strength, we realize a regime where three distinct phases can coexist in the same state: uniform superfluidity, modulated superfluidity, and discrete droplets. This work numerically investigates the vortex dynamics inside this multi-phase environment, mimicking the diverse conditions encountered at different radial depths within a neutron star.
[1] A. Melatos et al., ApJ 672, 1103 (2008).
[2] L. Warszawski and A. Melatos, MNRAS 415, 1611 (2011).
[3] E. Poli et al., Phys. Rev. Lett. 131, 223401 (2023).

Speaker: Héctor Briongos-Merino (University of Barcelona, ICCUB)

26 Pulse Profile Modulation due to Superfluid Phase Transition in the Pulsar Interior

Neutron star cores could host various novel phases, ranging from a nucleonic superfluid phase to exotic high-baryon-density quantum chromodynamics (QCD) phases. Several observational signals have been discussed in the literature for such phase transitions. The current work points to a unique phenomenon, the Kibble–Zurek mechanism, in which a superfluid vortex network forms during a phase transition to a superfluid phase, such as the nucleon superfluid or a phase like the color-flavor-locked phase. The random vortex network is transient and leaves behind the primary vortices that arise from the star's initial angular momentum. However, the transient, random vortex network can have a non-zero net angular momentum, which can be oriented in an arbitrary direction. Due to the conservation of angular momentum, the normal component gains an equal and opposite angular momentum, thereby imparting the arbitrarily oriented angular momentum to the rest of the neutron star. For pulsars, the induced angular momentum would alter the pulse timing and profile, and the associated modulation will decay systematically as the vortex network decay, following characteristic scaling behaviour that could serve as a universal indicator of superfluid transitions in the neutron-star core.

Speaker: DEEPTHI GODABA VENKATA (Birla Institute of Technology and Science, Pilani)

27 Microscopic GPE Calculations for Vortices Interaction in Neutron 1S0 and 3P2 Mixed Phase at the Crust-Core Boundary

Observations of neutron stars have revealed a rapid changing in rotation velocity, known as a “Glitch” phenomenon. The glitching mechanism is thought to be related to neutron superfluidity inside neutron stars. In the inner crust region, neutrons are $^1S_0$ superfluid. While in the outer core, they behave as $^3P_2$ superfluid, which may form half-Integer vortices [1]. Vortices in different regions connect with each other, and this can form a "network" of vortices consisting of a large number of vortices. This "vortex network" could be the key mechanism to explain the glitch phenomenon [2]. However, the microscopic structure of how these vortices connect across the inner crust and outer core boundary has not yet been investigated.
In this presentation, we describe the microscopic structure of neutron $^3P_2$ superfluid in the outer core of a neutron star using the Gross-Pitaevskii equation (GPE) and explain the shape of the neutron quantum vortex. Furthermore, we analyze how $^3P_2$ vortices in the outer core connect to $^1S_0$ vortices in the inner crust. Quantitatively evaluate the magnitude of the interaction between the vortices of the two regions.

[1] M.Kobayashi, M.Nitta, PRC 105, 035807 (2022)
[2] G. Marmorini, S. Yasui, M. Nitta, Scientific Reports, 14:7857 (2024)

Speaker: Tatsuhiro Hattori (Institute of Science Tokyo)

Outreach talk

Convener: Brynmor Haskell (Universita' degli Studi di Milano, Italy)

Wed, June 24

WG3 - Macroscopic scales - NS and their laboratory analogues: 1st morning session

Convener: Constança Providência

28 Neutron stars as cosmic laboratories for superfluid dynamics

Owing to the extreme densities, pressures and low (on the nuclear physics scale) temperatures of their interiors, neutron stars act as cosmic laboratories for superfluid dynamics. The theoretical motivation for this is well established and pulsar glitches – sudden spin-up events followed by a gradual relaxation – provide convincing observational support. Nevertheless, and despite about half a century of deliberation, we do not yet have robust theoretical models than can be directly tested against observations. In this talk, I will survey the problem and – at least try to – suggest ways that we may make progress.

Speaker: Nils Andersson

29 Tayler-Spruit dynamo, low-field magnetars and central compact objects

Low-field magnetars have dipolar magnetic fields of $10^{12}$--$10^{13}$ G, 10-100 times weaker than the values of magnetic-field strength $B\approx$ $10^{14}$--$10^{15}$ G used to define classical magnetars, yet they produce similar X-ray bursts and outbursts. Using direct numerical simulations of magnetothermal evolution starting from a dynamo-generated magnetic field, we show that the low-field magnetars can be produced as a result of a Tayler-Spruit dynamo inside a proto-neutron star. We find that these simulations naturally explain key characteristics of low-field magnetars: weak ($\leq 10^{13}$ G) dipolar magnetic fields, strong small-scale fields and magnetically induced crustal failures producing X-ray bursts. We run new simulations with different stratifications and magnetic Prandtl number as well as volumetric forcing. Some of these new simulations similarly produce low-B magnetars while other produce neutron star with properties similar to central compact objects.

Speaker: Dr Andrei Igoshev (Newcastle University)

10:40 AM Coffee Break

2nd morning session

Convener: Andrei Igoshev (Newcastle University)

30 Magnetic and Thermal Evolution of Neutron Stars with Superfluid and Superconducting Interiors

Neutron stars are ultra-dense remnants of massive stellar cores, observable across the electromagnetic spectrum. Their emission reflects a complex interplay of magnetic, thermal, and structural processes operating under extreme conditions of density, temperature, and magnetic field strength—regimes unattainable in terrestrial laboratories. Understanding isolated neutron stars requires studying the physics of their interiors, where neutrons are expected to form a superfluid and protons become superconducting—macroscopic quantum states that strongly influence both magnetic field evolution and neutron star cooling. In this talk, I will introduce MATINS, a new open-access 3D code designed to model the coupled magneto-thermal evolution of isolated neutron stars. I will first discuss neutron star cooling, with particular emphasis on how these macroscopic quantum states affect their thermal evolution. The second part of the talk focuses on the physics governing magnetic field evolution, with particular emphasis on magnetars and the origin of their observed large-scale dipolar magnetic fields. Finally, I will discuss the role of proton superconductivity in neutron star cores and its impact on magnetic field evolution, highlighting observable signatures that may arise from these exotic states of matter.

Speaker: Clara Dehman (University of Alicante)

31 Interior Magnetic field in Magnetars

Magnetars represent one of the most extreme environments in the universe, where magnetic forces are fundamentally important to understanding their behavior. These objects manifest through energetic transients such as Soft Gamma Repeaters and Anomalous X-ray Pulsars, yet the configuration and longevity of their internal magnetic architecture remain poorly understood.
I will present results from three-dimensional general relativistic magnetohydrodynamic simulations to investigate the evolution of magnetic fields in these systems. Our numerical survey explores how rotation rate and initial magnetic field strength independently and collectively influence magnetic instability development and the resulting field topology. By systematically varying these parameters, we disentangle their respective effects on the long-term stability and structure of magnetar magnetic fields. We identify two distinct evolutionary regimes depending on the interplay between rotation and magnetic field strength. Rapid rotation enables shear-driven growth of the azimuthal field, while highly magnetized systems develop poloidal instabilities that drive rapid field dissipation.

Speaker: Raj Kishor Joshi (CAMK, Warsaw, Poland)

32 Turbulence Modelling in Magnetised Neutron Stars

Turbulence is a key driver of dynamics in both isolated and binary neutron star (BNS) systems, and can be triggered by magnetic field instabilities. In particular the onset of the Kelvin-Helmholtz and Magnetorotational Instabilities plays a key role in the evolution of the magnetic field in a post-merger remnant from a BNS system. Modelling the impact of turbulence directly in numerical simulations of a BNS is impossible due to the small length scales involved, but the impact of turbulence on large scale physics can be incorporated through a subgrid model for turbulence. In this talk I will present a new such subgrid model, for Newtonian and Special Relativistic Magnetohydrodynamics, developed using machine learning techniques, and demonstrate its ability to capture the impact of turbulence on large scale magnetised fluid evolutions. This demonstrates the capability to deploy such a model in general relativistic simulations of Neutron Star spacetimes, capturing the impact of turbulence on magnetic field evolution and multimessenger observables.

Speaker: William Cook (FSU Jena)

12:50 PM Lunch

2:30 PM Free afternoon

Thu, June 25

Astro - generic: 1st morning session

Convener: Clara Dehman (University of Alicante)

33 Bulk viscosity and damping of density oscillations in binary neutron star mergers

Bulk viscosity in neutron stars plays an important role in the dynamics of binary neutron star mergers by damping density oscillations in the post-merger remnant. In this talk, I will review the computation of bulk viscosity in the warm, dense, neutrino-transparent cores of neutron stars for two possible compositions: nuclear matter and quark matter. For the nuclear matter equation of state (EoS), we employ relativistic density functional models with two representative parametrizations, DDME2 and NL3, which differ in the presence of the direct Urca threshold. For quark matter, we use the SU(3) Nambu–Jona-Lasinio (NJL) model extended by vector interactions and the ’t Hooft determinant term.
I will discuss the relevant weak-interaction processes in both nuclear and quark matter that give rise to bulk viscosity under merger conditions. I will then outline the derivation of the corresponding bulk viscosity coefficients and discuss the associated damping rates of density oscillations in binary neutron star mergers. Finally, I will address how bulk-viscous dynamics, potentially encoded in future observational data, may provide a probe of the microscopic composition and equation of state of neutron star interiors, including signatures associated with the onset of the direct Urca processes.

Speaker: Dr Arus Harutyunyan (Byurakan Astrophysical Observatory, Yerevan State University)

34 Beyond the Taylor Expansion: Systematics in the phase of continuous gravitational wave

Studying isolated asymmetric neutron stars via continuous gravitational waves has become a new approach to understanding neutron star physics, given improvements in detector sensitivity and the upcoming next-generation detectors like the Einstein Telescope, which will make detection of these signals feasible in the near future. In our work, we investigate whether corrections to the gravitational wave phase beyond the simple rotating ellipsoid model affect results and how they would bias constraints on our detections, thereby improving our search pipelines. These phase contributions can arise from any physical effects such as spin wandering, timing noise and lensing of continuous waves.

Speaker: Anirudh Nemmani (Nicolaus Copernicus Astronomical Center, CAMK PAN)

35 Self-consistently connecting the neutron star mode spectrum to fundamental nuclear physics

Neutron star (NS) asteroseismology is a powerful tool for probing the nature of matter inside NSs, with various oscillation modes being sensitive to different properties of matter in different regions of the star, and thus to different aspects of fundamental nuclear physics. Current asteroseismic studies however focus on particular families of oscillation modes, or rely on phenomenological parametrisations that obfuscate links to the underlying physics of nuclear interactions responsible for properties of NS matter. While this has been sufficient to examine previous asteroseismic observables, planned next-generation gravitational wave (GW) observatories -- such as the Einstein Telescope (ET) or Cosmic Explorer (CE) -- will be sufficiently sensitive to detect the impact of resonant and off-resonant excitations of a wide range of modes in many binary NS sources, providing an unprecedented amount of information about the NS mode spectrum. To fully utilise this information, we must work to develop models that self-consistently derive a wide range of NS matter properties from underlying nuclear physics, allowing for modes across the spectrum to be consistently calculated and linked to fundamental physics. Neutron superfluidity is of particular note for this, as it results in the appearance of an entire new class of modes with counter-moving fluid and superfluid elements. In this talk, I will give an overview of the neutron star mode spectrum and the wide range of physics -- including neutron superfluidity -- on which it depends, discuss previous works that incorporated superfluidity into the calculation of mode frequencies and eigenfunctions, and examine challenges in self-consistently connecting the full NS mode spectrum that will be observable in GWs to fundamental nuclear physics.

Speaker: Duncan Neill (University of Bath)

10:40 AM Coffee Break

2nd morning session

Convener: Gary Liu (Department of Physics, Royal Holloway University of London)

36 Measuring the crust-superfluid coupling time-scale for 105 UTMOST pulsars

Crust-superfluid coupling plays an important role in neutron star rotation, particularly with respect to timing noise and glitches. Here, we present new timing-noise-based estimates of the crust-superfluid coupling timescale $\tau$ for 105 radio pulsars in the UTMOST dataset, by Kalman filtering the pulse times of arrival. The 105 objects are selected because they favour a two-component, crust-superfluid model over a one-component model with log Bayes factor ⁠over 5. The $\tau$ posteriors are sharply peaked among 28 out of 105 objects. Population-level scaling of $\tau$ as functions of the angular velocity $\Omega_{\rm c}$ and spin-down rate $\dot{\Omega}_{\rm c}$ of the crust is estimated among 101 out of 105 objects that are canonical. Implications for the crust-superfluid coupling through mutual friction are briefly discussed.

Speaker: Wenhao Dong (University of Melbourne & OzGrav)

37 Constraining neutron star properties with current and future gravitational wave observations of glitching pulsars

Rapidly rotating pulsars are known to undergo spontaneous increases in their rotation frequency known as "glitches" which interrupt their normal spindown rate. While the precise mechanism is unknown, this process is believed to be due to an internal exchange of angular momentum. Such a process may cause the emission of gravitational waves across multiple frequency bands and timescales which could offer valuable insights on the internal superfluid structure of these stars. In this talk, we present the results of a search for gravitational waves from the 2024 Vela pulsar glitch across multiple timescales with data from the fourth LIGO-Virgo-KAGRA observing run and the astrophysical implications of the results. We also discuss how next-generation gravitational wave detectors could teach us more about the internal structure and possibly superfluid effects.

Speaker: Matthew Ball

38 Superfluid vorticity, Magnus mountains, and gravitational waves

Rotating neutron stars, if deformed away from axisymmetry, produce long-lived gravitational waves. One possible source for such “mountains” is a non-axisymmetric distribution of the neutron superfluid’s vorticity, sustained by vortex pinning to the star’s solid outer crust, or to the magnetic flux tubes in the core. The Magnus force generated distorts the star, giving what we term a “Magnus mountain”. We model this process in an idealised geometry, computing the mass asymmetry generated. Our results will be of use in building more realistic models of Magnus mountains, and help open up a new avenue to probe superfluidity via gravitational wave observations.

Speaker: Ian Jones (University of Southampton)

12:50 PM Lunch

NS crust: 1st afternoon session

Convener: Nils Andersson

39 Vortex Avalanches in Neutron Stars

Vortex avalanches are believed to cause pulsar glitches, with $10^{17}$ of quantum vortices transferring angular momentum from the inner-crust superfluid to the crust of a pulsar. In this presentation, we investigate the vortex avalanches using the Gross-Pitaevskii model for a system with more than $600$ vortices in a linearly spin-down superfluid. For the first time, we showed that during vortex avalanches, up to $\approx40$ vortices can be collectively involved in a glitch, followed by a post-avalanche dynamics that vortices redistribute with orbiting motions around large vortex density voids. In order to scale up the system size and number of vortices, we then adapt the point-vortex model to simulate the vortex-dominated system and found an effective range of parameters that can reproduce similar dynamics and comparable statistics to the quantitative level. Lastly, we discuss the possibility of generating much larger avalanches.

Speaker: Gary Liu (Department of Physics, Royal Holloway University of London)

40 Entrainment effects in the inner crust and outer core of a neutron star

The neutron superfluid present in the inner crust and outer core of a neutron star is coupled to the rest of the star due to nondissipative entrainment effects of different nature. Such effects could play an important role in the dynamics of the star. In the crust, entrainment effects are measured in terms of the superfluid density, i.e. the density of neutrons that contribute to the superfluid motion, or equivalently in terms of an effective mass of crustal ions. Both are derived in the linear response theory within the Bardeen-Cooper-Schrieffer approximation. The superfluid density thus obtained leads to the same entrainment matrix as derived earlier in homogeneous neutron-proton superfluid mixture, thus providing a unified description of entrainment effects throughout the inner crust and outer core within the same microscopic framework. The superfluid density and effective ion mass are evaluated numerically in different regions of the crust from three-dimensional band-structure calculations, taking into account lattice vibrations. Results are compared to predictions from classical hydrodynamics with different prescriptions for the permeability of ions to superfluidity.

Speaker: Nicolas CHAMEL (Université Libre de Bruxelles, Belgium)

41 Vortex-nucleus interaction in the inner crust of neutron star

Astronomical observations of neutron stars provide information on kilometer scales, while the nuclear interactions that govern their properties operate on femtometer scales. Describing physical processes across such vastly different length scales requires effective theoretical models. The inner crust of a neutron star is a particularly complex system, where a lattice of nuclei strongly interacts with vortices which are collective excitations in the neutron superfluid. Developing an effective description of this environment requires a detailed understanding of the vortex–nucleus pinning force.

In this work, we use a microscopic approach based on time-dependent density functional theory to study the force between a vortex and a nucleus. Using modern nuclear density functionals designed for astrophysical applications, we simulate nuclear matter across different layers of the inner crust in an unconstrained three-dimensional geometry with a volume of 500,000 fm³. We also release the raw simulation data to help bridge microscopic and mesoscopic predictions, and to support the development and benchmarking of astrophysical models such as vortex filament models.

Speaker: Daniel Pęcak (Institute of Physics, Polish Academy of Sciences)

4:10 PM Coffee Break

2nd afternoon session

Convener: Ian Jones (University of Southampton)

42 Superfluid fraction in the inner crust of neutron stars

Neutron stars are fascinating astrophysical objects, containing matter at densities that exceeds the density of atomic nuclei. Among the most puzzling phenomena associated with them are pulsar glitches. Pulsars are rapidly rotating neutron stars, emitting beams of radiation from their magnetic poles and acting as the most precise clocks in the Universe, even surpassing the accuracy of atomic clocks on Earth. Occasionally, however, they exhibit sudden increases in their rotational frequency, events known as glitches.
These unexpected spin-ups are thought to arise from complex interactions between different internal components of the star. Several theoretical models have been proposed to explain glitches, most of them relying on superfluidity in parts of the star [1].
This talk will focus on the neutron stars crust, which is thought to be a lattice of nuclear clusters immersed in an electron gas. The transition from the outer to the inner crust is where neutrons begin to "drip" from nuclei, eventually leading to a superfluid neutron gas between the nuclear clusters [2].
The exotic phases within the inner crust are central to the star thermal and hydrodynamic behavior. This talk focuses on a quantum mechanical description of the inner crust. A central aspect is determining the superfluid density, which is a quantity directly related to the effective mass of nuclear clusters moving through the neutron gas.
I will present the Hartree-Fock-Bogoliubov calculations with Bloch boundary conditions which we used to model the inner crust [3, 4, 5]. In order to get the most reliable results, modern energy density functionals have been implemented, together with a realistic pairing interaction.
For the extraction of the superfluid density, a framework based on a Galilean transformation is constructed, allowing one to get this quantity within a time-independent calculation.
Together with fully self-consistent numerical results, I will present the expression for the superfluid density which we derived in the Bardeen-Cooper-Schrieffer approximation [6]. This allows one to evaluate this quantity directly from the single-particle band structure, thus offering a benchmark for complete results and providing insight into the interplay between periodicity and superfluidity. In this framework, we showed the importance in the inner crust of the so-called geometric contribution to the superfluid density, which is known to be relevant also in ultra-cold atoms [7] and high-temperature superconductors [8].
Our results suggest that about 90% of the neutrons are effectively superfluid, making possible to explain glitches with models that involve the crust only.

[1] P. W. Anderson and N. Itoh, Nature 256, 25–27 (1975).
[2] N. Chamel and P. Haensel, Liv. Rev. Relativity 11, 10 (2008).
[3] G. Almirante and M. Urban, Phys. Rev. C 109, 045805 (2024).
[4] G. Almirante and M. Urban, Phys. Rev. C 110, 065802 (2024).
[5] G. Almirante, T. Kaskitsi, and M. Urban, Phys. Rev. C (2026).
[6] G. Almirante and M. Urban, Phys. Rev. Lett. 135, 132701 (2025).
[7] S. Peotta and P. Torma, Nat. Commun. 6, 8944 (2015).
[8] M. Iskin, Phys. Rev. B 109, 174508 (2024).

Speaker: Giorgio Almirante

43 Josephson currents in neutron stars

We demonstrate that the interface between S-wave and P-wave paired
superfluids in neutron stars induces a neutron supercurrent, a
charge-neutral analog of the Josephson junction effect in electronic
superconductors. The proton supercurrent entrainment by the neutron
superfluid generates, in addition to the neutral supercurrent, a
charged current across the interface. Beyond this stationary effect,
the motion of the neutron vortex lines responding to secular changes in
the neutron star's rotation rate induces a time-dependent oscillating
Josephson current across this interface when proton flux tubes are
dragged along with them. We show that such motion produces radiation
from the interface once clusters of proton flux tubes intersect the
interface. The power of radiation exceeds by orders of magnitude the
Ohmic dissipation of currents in neutron stars. This effect appears to
be phenomenologically significant enough to heat the star and alter its
cooling rate during the photon cooling era.

Speaker: Armen Sedrakian (University of Wroclaw and FIAS)

44 Hydrodynamic Simulation of Glitches in Neutron Star Crusts

Many neutron stars exhibit rotational 'glitches' caused by the collective depinning of $>10^7$ superfluid vortices. Gross–Pitaevskii (GP) and point-vortex (PV) simulations have demonstrated glitching behaviour via development of vortex avalanches with $500$-$5000$ vortices. Given that a real neuron star contains more than $>10^{13}$ vortices, simulating glitches in a global-scale model requires averaging over many vortices. We develop a hydrodynamic model describing the evolution of vortex density in terms of pinned and free components. The corresponding system of partial differential equations is solved using the pseudospectral method with Dedalus v3 code. We find that multiple glitches arise as hydrodynamic shear instabilities within a certain parameter regime, and are qualitatively similar to dynamics seen in GP and PV simulations. These results suggest that vortex avalanches persist in a coarse-grained model, representing a step toward bridging microscopic and macroscopic descriptions of neutron star crusts.

Speaker: Mr Charlie Perkins (Newcastle University)

MC meeting

Conference dinner

Fri, June 26

NS - generic: 1st morning session

Convener: Armen Sedrakian (University of Wroclaw and FIAS)

45 The dense-matter equation of state from cold neutron stars to protoneutron stars: status, methods, and signatures

The equation of state (EoS) of strongly interacting matter at the densities reached inside neutron stars (NSs) sits at the interface of low-energy nuclear theory, perturbative QCD, and multi-messenger astronomy. In this talk I will first review the current status of the zero-temperature EoS and the constraints that shape it: chiral effective field theory below nuclear saturation, perturbative QCD at asymptotically high densities, and the present generation of astrophysical observations — NICER mass–radius measurements of PSR J0030+0451, J0740+6620, J0437–4715 and J0614–3329, together with the tidal-deformability information from GW170817. I will then contrast the two complementary strategies used to translate these data into an EoS: model-agnostic schemes (c²s interpolation, fractal-bridge priors, etc.) and microscopic relativistic mean-field approaches with density-dependent or nonlinear meson couplings. Within this framework, I will briefly discuss results from our recent Bayesian studies — in particular a systematic cross-comparison of covariant energy-density functionals. I will close by extending the discussion to finite temperature, where Bayesian-constrained nucleonic and hyperonic mean-field EoSs are used to follow protoneutron-star evolution, characterise the thermal index, and translate maximum-mass measurements into indirect bounds on the hyperonic content of NS cores.

Speaker: Mr Tuhin Malik (CFisUC, Department of Physics, University of Coimbra)

46 Statistical Analysis of Neutron Star Cooling: Implications for the Nuclear Equation of State and Nucleon Pairing

We perform a statistical analysis of the thermal evolution of isolated neutron stars (NSs) by confronting theoretical cooling curves with luminosity–age measurements for 24 sources. For each object, we explore five purely nucleonic equations of state—APR4, FSU2R, DD2, IST, and NL3$\omega\rho$—combined with representative models of neutron superfluidity and proton superconductivity, while varying the gravitational mass and envelope composition. The analysis spans approximately $10^4$ cooling curves. Within this framework, we find that only the NL3$\omega\rho$ equation of state and, to a lesser extent, IST - both including neutron triplet pairing—provide an overall satisfactory description of the data. The remaining equations of state are in significant tension with the observations. These results indicate that neutron star cooling can place nontrivial constraints on dense matter, favoring specific combinations of the equation of state and nucleon pairing properties.

Speaker: Afonso Ávila (University of Coimbra)

47 How effectively can Neural Posterior Estimation infer the Neutron Star Equation of State?

The equation of state (EoS) of neutron star matter encodes the relationship between pressure and density at supranuclear densities, fundamentally governing the star’s structure and observable macroscopic properties, such as mass, radius, and tidal deformability. In this work, we apply Neural Posterior Estimation (NPE) with conditional normalising flows to infer the EoS from synthetic observational data. We consider a model-agnostic EoS family and train our models on mock mass-radius
and mass-radius–tidal deformability datasets with varying noise levels. We evaluate reconstruction performance in terms of pressure and squared speed of sound across baryonic densities, and
quantify the impact of including tidal deformability information. Our results demonstrate that tidal
measurements significantly reduce inference uncertainty, particularly for pressure, and confirm that
NPE-based models can accurately capture physical constraints.

Speaker: Valéria Carvalho

10:40 AM Coffee Break

2nd morning session

Convener: Tuhin Malik (CFisUC, Department of Physics, University of Coimbra, Portugal)

48 Black hole microstates and strongly coupled hydrodynamics

We construct a description of hydrodynamics and superfluidity for a class of strongly coupled conformal (quantum critical) systems within the framework of gauge/gravity duality (holographic duality). We first review the basic idea of holographic duality and the state-of-the-art results on holographic superfluids, which are dual to black holes with thermal horizons. We then extend these results to smooth microstate geometries. In a particular setup of AdS bubbling geometries we compute the diffusion coefficient and viscosity and compare them to universal bounds for black holes. Finally, we discuss possible applications to astrophysical systems.

Speaker: Mihailo Cubrovic (Institute of Physics Belgrade)

49 Calibrating the medium effects of light clusters in heavy-ion collisions

Light nuclei are found in core-collapse supernova matter and in binary neutron star mergers. Their abundance can affect the dynamics and properties of supernovae [1-3] and binary neutron star mergers [4-8], both directly through their weak reactions with the surrounding medium, and indirectly through their competition with heavy nuclei [9], which can modify the proton fraction and the size of nucleosynthesis seeds [10]. They can also have a significant (indirect) effect on the dynamics of the core-collapse supernova explosion giving rise to a faster shock retreat and an early neutrino luminosity [11], even though, only a negligible (direct) impact from the weak reactions involving the light clusters was obtained. The transport coefficients are determined by the collision rates of electrons and/or neutrinos with clusters, which in turn depend on the cluster abundances and sizes. In binary mergers, the recombination of free nucleons into particles can generate enough energy to induce mass outflows [12]. Therefore, the study of light nuclei is essential to obtain a good description of these astrophysical events. In particular, in the scope of relativistic mean-field models, their nuclear couplings need to be calibrated to experimental data such as heavy-ion collisions. In this work [15], we propose a Bayesian inference estimation of in-medium modification of the cluster self-energies from light nuclei multiplicities measured in selected samples of central XeSn collisions with the INDRA apparatus. The data are interpreted with a relativistic quasi-particle cluster approach in the mean-field approximation without any prior assumption on the thermal parameters of the model. An excellent reproduction is obtained for H and He isotope multiplicities, and compatible posterior distributions are found for the unknown thermal parameters, for two different nuclear models.

[1] A. Arcones, G. Martínez-Pinedo, E. O’Connor, A. Schwenk, H.-T. Janka, C. J. Horowitz, and K. Langanke, Phys. Rev. C 78, 015806 (2008).
[2] K. Sumiyoshi and G. Roepke, Phys. Rev. C 77, 055804 (2008).
[3] S. Furusawa, H. Nagakura, K. Sumiyoshi, and S. Yamada, Astrophys. J. 774, 78 (2013).
[4] A. Bauswein, S. Goriely, and H. T. Janka, Astrophys. J. 773, 78 (2013).
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Speaker: Mr Tiago Custódio

50 Bayesian inference of hybrid stars with large quark cores

Neutron stars (NSs) are interesting objects capable of reaching densities unattainable on Earth. The properties of matter under these conditions remain a mystery. Exotic matter, including quark matter, may be present in the NS core. In this work, we explore the possible compositions of NS cores, in particular, the possible existence of large quark cores. We use the relativistic mean-field (RMF) model with nonlinear terms for the hadron phase and the Nambu–Jona-Lasinio (NJL) model and mean-field theory of quantum chromodynamics (MFTQCD) for the quark phase. Through Bayesian inference, we obtain different sets of equations: four sets with hybrid equations and one set with only the hadron phase. We impose constraints regarding the properties of nuclear matter, x-ray observational data from NICER, gravitational wave data from the binary neutron star merger GW170817, perturbative QCD calculations, and causality. The MFTQCD allows for a phase transition to quark matter at low densities, just above saturation density, while for the NJL sets, the phase transition occurs above twice the saturation density. As a result, the MFTQCD model predicts the presence of quark matter in the inner core of 1.4 $M_\odot$ NSs, while NJL models suggest a low probability of quark matter in the interior of a 1.4 $M_\odot$ NS. Both models predict the existence of quark matter in 2 $M_\odot$ NSs. The slope of the mass-radius curve has been shown to carry information about the presence of quark matter. In particular, a positive slope at 1.8 $M_\odot$ indicates the presence of non-nucleonic matter. A hybrid star with a stiff quark equation of state could explain a larger radius in more massive stars, such as two solar mass stars, compared to canonical NSs.

Speaker: Milena Albino (University of Coimbra)

12:50 PM Lunch

1st afternoon session

Convener: Mihailo Cubrovic (Institute of Physics Belgrade)

51 From effective field theories of higher-form symmetries to neutron stars and superfluids

In this talk, I will review recent progress in formulating effective field theories for hydrodynamic-like states with higher-form symmetries. These symmetries are associated with the conservation of extended objects that constitute the fluid. One example is a plasma composed of one-dimensional strings, or magnetic flux lines, whose dynamics are described by magnetohydrodynamics. I will discuss different classes of such theories and present our new formulation of magnetic diffusion in neutron stars. A closely related framework can also be applied to superfluids, providing a novel perspective on their dynamics. In the final part of the talk, I will present recent results on the physics of superfluids and conclude with a discussion of open problems related to the description of superfluids in neutron stars.

Speaker: Saso Grozdanov (University of Edinburgh, University of Ljubljana)

52 Amortized Neural Posterior Estimation for Relativistic Mean-Field Constraints on the Neutron-Star Equation of State

We present an amortized (train-once-use-many) simulation-based inference framework for constraining the nuclear equation of state of neutron stars within density-dependent relativistic mean-field models. The aim is to validate Neural Posterior Estimation (NPE) as a fast alternative to conventional nested-sampling analyses, while preserving full Bayesian posterior quantification. We benchmark two RMFs, one with density-dependent couplings (DDB) and the other with constant nonlinear couplings (RMF-NL), against a PyMultiNest reference analysis using recent empirical nuclear-matter constraints and the two-solar-mass neutron-star requirement. Training sets of 2--3 million simulator pairs generated with the CompactObject framework are used to train a noise-conditional Neural Spline Flow, allowing observational uncertainties to be incorporated directly during training. The key advantage of this approach is amortization: after a one-time training cost, the same trained network can be conditioned on future observations and produce posterior samples within seconds, without rerunning the full sampler. A fully differentiable JAX-GPU forward model further enables rapid posterior propagation to mass--radius--tidal-deformability predictions and importance-sampling diagnostics. Preliminary DDB results show close agreement with PyMultiNest, with $M_{\max}=2.176$ vs.\ $2.141,M_{\odot}$, $R_{1.4}=12.81$ vs.\ $12.65~\mathrm{km}$, and $\Lambda_{1.4}=512$ vs.\ 466, together with successful SBC and TARP calibration tests. To our knowledge, this is the first direct amortized-NPE framework for RMF-based neutron-star EoS inference benchmarked against a nested-sampling reference, offering a scalable route for rapid reanalysis as nuclear and multi-messenger constraints evolve, particularly in view of next-generation observatories such as the Einstein Telescope and other upcoming gravitational-wave detectors.

Speaker: Prashant Thakur (Yonsei University)

53 Hybrid star with the NJL model using a density-dependent vector coupling

Neutron stars are objects described by the quantum chromodynamics (QCD), which predict a deconfined quark phase for high densities. It is possible that quark matter can be reached in the core of neutron star surrounded by a hadronic phase. For an hybrid star, the two solar mass neutron star constraint requires a stiff equation of state (EoS) for intermediate densities that supports a soft core at high densities. We use the density-dependent meson-nucleon – DDME2 model for the hadronic phase and the Nambu–Jona-Lasinio SU(3) model with multiquark interaction for quark phase with a density-dependent vector coupling – $G_{\omega \omega}(\rho_B)$ – such that at high densities it strongly weakens. The choice of this coupling is based on the strong constraints imposed by perturbative QCD (pQCD). We use Bayesian inference to construct sets of quark EoS constrained by x-ray observational data from NICER, gravitational wave data from the binary neutron star merger GW170817. The Maxwell construction is applied for the deconfinement phase transition. We compare hybrid star model with a model with a $G_{\omega \omega}$ not depending on density. We can see how the multiquark parameters are changed by this new configuration and discuss the behavior of the speed of sound. The EoS built all satisfy pQCD constraints although the constraint did not enter the Bayesian inference.

Speaker: Rafael Cardoso (Federal University of Santa Catarina and University of Coimbra)

4:10 PM Coffee Break

2nd afternoon session

Convener: Saso Grozdanov (University of Edinburgh, University of Ljubljana)

54 Role of the δ meson in the direct Urca cooling of neutron stars

In our work, we use bayesian inference to study how the inclusion of a scalar-isovector interaction channel within a RMF framework can affect the threshold for the direct URCA process in the core of neutron stars. We also study the effect of proton pairing by including a simplified model for the proton 1S0 pairing gap. The results show that the inclusion of the new interaction channel can significantly broaden the distribution of the threshold, allowing for direct URCA even in stars below 2 solar masses.

Speaker: Luigi Scurto (Laboratori Nazionali del Sud, Infn)

55 Investigating the nuclear matter equation of state with neutron stars

Neutron star interiors are very interesting environments to probe the nuclear matter equation of state (EOS), especially at the limit of high density and temperature. In this talk, I will discuss two approaches to constraining the neutron star EOS. The first approach consists of constraining the EOS with observations of neutron star mass, radius, and tidal deformability. I will explain how data from the NICER telescope and the LIGO-VIRGO interferometers are used for this purpose, and how constraints from ab initio calculations - such as chiral effective field theory (cEFT) and perturbative QCD (pQCD) – are incorporated to perform EOS inference. I will also discuss how the recent implementation of cEFT calculations including uncertainties obtained with Gaussian processes updated our knowledge of the high-density EOS behavior and enabled the inference of EOS parameters. The second approach to investigating the EOS is related to neutron star cooling and how X-ray astrophysical observations can be used to infer the evolution of neutron star luminosity over time. This kind of data can constrain other EOS quantities, such as particle composition and nuclear pairing. In particular, I will discuss how the luminosity of fast cooling, transiently-accreting neutron stars can be used to investigate a possible first-order quark-hadron phase transition.

Speaker: Melissa Mendes (Technische Universität Darmstadt)

56 Persistent gravitational radiation from glitching pulsars

Neutron star glitches may be caused by the sudden unpinning and collective movement of vortices in the superfluid condensate inside the star, also known as vortex avalanches. The metastable vortex configuration between avalanches is determined by the far-from-equilibrium avalanche dynamics and is nonaxisymmetric in general, producing a small but nonzero current quadrupole moment which generates persistent, quasi-monochromatic gravitational waves as it rotates. In this work, we use an N-body simulation of vortex avalanches to calculate an empirical scaling of this current quadrupole, and extrapolate that scaling to estimate the characteristic wave strain for this mode of emission. We also develop analytic upper- and lower-bound characteristic wave strain, which corresponds to idealized regimes in vortex dynamics and bracket the empirical scaling.

Speaker: Thippayawis Cheunchitra (The University of Melbourne)

Closing