Speaker
Description
We study the defocusing nonlinear Schrödinger (dNLS) equation, an integrable nonlinear partial differential equation ubiquitous in physics. This equation with nonzero boundary conditions admits soliton solutions: stable localised oscillations that scatter elastically. In the limit of a large number of solitons with random amplitudes, velocities and positions, called soliton gas, it is more relevant to characterise the resulting field by thermodynamic quantities, such as the average values of some observables, or the correlation functions.
The framework of Generalised Hydrodynamics (GHD) has allowed for the description of the many-body behaviour of classical and quantum particle integrable systems [1, 2], with remarkable agreement between the theory and the experiments [3]. The GHD for dNLS has already been built from the semi-classical limit of the Lieb-Liniger model, based on the radiative (non-solitonic) solutions of dNLS [4]. We derive a complementary GHD based on classical heuristic arguments, considering the solitons as point-like particles, which makes the statistical mechanics approach more natural and transparent. The exact procedure is similar to what has already been done for the Korteweg de Vries and Boussinesq equations [5, 6].
From an ansatz on the form of the partition function, we recover the soliton gas equivalent of the Yang-Yang equation, as well as expressions for the conserved charges and the two-point correlation functions in terms of the density of solitons. The soliton based formalism allows us to analytically solve the dressing equation for a particular class of soliton gases called dilute condensates, which we use to benchmark efficient numerical methods for the computations.
[1] - Bertini, B., Collura, M., De Nardis, J., & Fagotti, M. (2016). Transport in Out-of-Equilibrium X X Z Chains : Exact Profiles of Charges and Currents. Physical Review Letters, 117(20), 207201. https://doi.org/10.1103/PhysRevLett.117.207201
[2] - Castro-Alvaredo, O. A., Doyon, B., & Yoshimura, T. (2016). Emergent Hydrodynamics in Integrable Quantum Systems Out of Equilibrium. Physical Review X, 6(4), 041065. https://doi.org/10.1103/PhysRevX.6.041065
[3] - Dubois, L., Thémèze, G., Dubail, J., & Bouchoule, I. (2026). Experimental investigation of a bipartite quench in a 1D Bose gas. SciPost Physics, 20(1), 008. https://doi.org/10.21468/SciPostPhys.20.1.008
[4] - Del Vecchio Del Vecchio, G., Bastianello, A., De Luca, A., & Mussardo, G. (2020). Exact out-of-equilibrium steady states in the semiclassical limit of the interacting Bose gas. SciPost Physics, 9(1), 002. https://doi.org/10.21468/SciPostPhys.9.1.002
[5] - Bonnemain, T., Doyon, B., & El, G. (2022). Generalized hydrodynamics of the KdV soliton gas. Journal of Physics A: Mathematical and Theoretical, 55(37), 374004. https://doi.org/10.1088/1751-8121/ac8253
[6] - Bonnemain, T., & Doyon, B. (2025). Soliton gas of the integrable Boussinesq equation and its generalised hydrodynamics. SciPost Physics, 18(2), 075. https://doi.org/10.21468/SciPostPhys.18.2.075