# Collection 2024 - T1 - Quantum many-body systems out-of-equilibrium

The theoretical study of quantum many-body systems is a challenging task due to the amazing complexity induced by the huge number of degrees of freedom of these systems. Equilibrium properties of such systems have been deeply studied in the last decades. In particular, at one-dimension, it is possible for some systems to have access to exact solutions, for instance, within Bethe Ansatz methods. Where exact solutions are not accessible, it is possible to use field theoretical approaches or numerical techniques. Even if, formally, it is possible to have exact solutions both at zero and finite temperature, the case of finite (low) temperature can be exceptionally complicated for quantum mixtures, where one should solve an infinite number of coupled equations following a Bethe Ansatz scheme. Although equilibrium at zero temperature is an ideal situation, most of the physical systems are out-of-equilibrium and/or at finite temperature. Indeed in the last years, several communities have concentrated their effort in the study of quantum many-body systems out-of-equilibrium, both close and open. From the mathematical point of view, a lot of progress has been made recently regarding the asymptotic expansion of the many-body Schrödinger equation in macroscopic limits (correlation energies, quantum fluctuations...). Important challenges remain, in particular as regards applications to scaling limits most relevant for experiments, such as the so-called Gross-Pitaevskii limit for bosons.

The aim of this trimester is to give the possibility to the scientists of these different communities to meet, share their advances, create new collaborations and make theoretical frames and mathematical tools progress.

**Organizer(s)**Fazio, Rosario ; Giamarchi, Thierry ; Minguzzi, Anna ; Vignolo, Patrizia

**Date(s)**08/01/2024 - 22/03/2024

**linked URL**https://indico.math.cnrs.fr/event/8995/