Speaker
Description
We consider quantum or classical many-body Hamiltonian systems characterized by integrable
contact interactions supplemented by a generic two-body potential, potentially long-range. We
show how the hydrodynamics of local observables is given in terms of a generalised version of Bogoliubov–Born–Green–Kirkwood–Yvon
hierarchy, which we denote as gBBGKY, which is built for the
densities, and their correlations, of the quasiparticles of the underlying integrable model. Unlike the
usual cases of perturbation theory from free gases, the presence of local interactions in the integrable
model “lifts” the so-called kinetic blocking, presenting thermalization time scales quadratic in the perturbing potential.
In particular, we check our results with exact molecular dynamics simulations for the perturbed Hard rod gas, finding convincing agreement.
Unlike previous approaches based on Fermi’s golden rule and matrix elements, the
gBBGKY allows one to directly access the late time scattering integrals and the time evolution of multi-point
correlations in generic perturbed integrable models at hydrodynamic length and time scales.
It can be also applied to systems on a lattice such as long-range spin chains or fermionic systems as first experimentally driven examples.
Finally, we show how it can be straightforwardly extended to interacting multi-tubes systems, already implemented in cold-atoms experiments.
