Appears in collection : 2024 - T1 - Quantum many-body systems out-of-equilibrium

In this seminar I will discuss the physics of interacting bosons on a ring. I will first consider the stability of metastable current states, in a presence of a localized barrier. In particular I will show that for large barriers a universal dynamics emerges that involves dispersive shock waves, at all interaction strengths, that can be understood using the generalized hydrodynamics framework. I will then focus on the weak barrier regime and show that the dynamics is non-universal and involves in the mean-field regime thermally activated grey solitons. In a second part I will introduce the tools of the inverse scattering transform to study far from equilibrium states and discuss how they can be adapted to the ring geometry. Finally I will conclude by pointing out a few perspectives in the study of non-integrable systems and soliton gases.