Stationary states and non-thermal behaviour in superfluids out of equilibrium

Peter Barmettler, Corinna Kollath

We analyse the stationary behaviour of correlations in a strongly correlated Bose gas out of equilibrium. The dynamics are triggered by a quench of the interaction starting from the strongly interacting limit where the system is in a perfect Mott state. Despite the complete integrability of our theoretical description, we find seemingly thermal behaviour for the experimentally measurable correlations at large interactions. Quite opposed, away from the strongly interacting regime these correlation functions show highly non-thermal stationary values. This behaviour is explained by overlaps of the integrals of motion with the observable and the initial state in an effective thermal ensemble. These results suggest that non-equilibrium Mazur equalities are an efficient way to calculate short range correlations for arbitrary integrable models.

Fabio Anza, Cameron Hahn

Projected ensembles---the collections of conditional pure states induced on a system by measuring an entangled environment---have become central objects in quantum science, underlying deep thermalization, quantum state designs, the emergence of classicality, and exhibiting interesting phase transitions. Here we develop a general and exact theory of their dynamics, yielding a systematic approach to their dynamics and equilibrium and non-equilibrium stationary states. We derive an exact continuity equation on quantum state space for the projected ensemble, together with microscopic kinetic equations and analytical expressions for the probability flux and source terms generated by the system-environment interaction. The resulting dynamics admits a classical representation: isolated systems obey Hamiltonian transport and Liouville's theorem, while open systems are described by a kinetic theory of probability transport. The stationary continuity equation provides a general characterization of equilibrium and non-equilibrium stationary projected ensembles, which can be analyzed through the method of characteristics. The theory provides an analytical framework for studying the emergence, structure, and timescales of equilibrium and non-equilibrium stationary projected ensembles, with applications ranging from deep thermalization and the emergence of classicality to random quantum-state generation and quantum device benchmarking.

Marine Pigneur

Maxim Dzero, Emil A. Yuzbashyan, Victor Gurarie

Sascha Wald, Malte Henkel, Andrea Gambassi

Abstract The collective and purely relaxational dynamics of quantum many-body systems after a quench at temperature T = 0, from a disordered state to various phases is studied through the exact solution of the quantum Langevin equation of the spherical and the O ( n )-model in the limit n → ∞. The stationary state of the quantum dynamics is shown to be a non-equilibrium state. The quantum spherical and the quantum O ( n )-model for n → ∞ are in the same dynamical universality class. The long-time behaviour of single-time and two-time correlation and response functions is analysed and the universal exponents which characterise quantum coarsening and quantum ageing are derived. The importance of the non-Markovian long-time memory of the quantum noise is elucidated by comparing it with an effective Markovian noise having the same scaling behaviour and with the case of non-equilibrium classical dynamics.