Long-time relaxation of open quantum many-body systems
Alice Marché
In this thesis, we investigate the relaxation of quantum many-body dissipative systems, initially far from equilibrium. We focus on Markovian systems whose dynamics are governed by a Lindbladian and analyze how they approach their stationary states at long times. The results presented in this work are twofold. Firstly, we study systems governed by gapless Lindbladians, which exhibit critical slowing down of their relaxation dynamics. We derive analytical predictions for this slow decay in two different settings: two bosons undergoing local two-body losses, either in the continuum or on a one-dimensional lattice, and a spin-1/2 chain with non-reciprocal hopping described by two-site correlated dissipation. Secondly, we investigate how symmetries constrain the dynamics and stationary states of dissipative quantum systems, allowing them to retain partial memory of their initial conditions. In particular, we analyze a dephasing model that hosts, together with the maximally mixed state, an additional stationary state associated with a non-extensive strong symmetry, displaying a phenomenology similar to that of quantum many-body scars in closed systems. We also study an SU(3)- invariant Fermi–Hubbard gas subject to on-site three-body losses. We show that this system exhibits a rich structure of symmetry-protected dark states, which can be characterized using semistandard Young tableaux.
Jury : Jérôme Dubail (rapporteur), Hosho Katsura (invité), Zala Lenarčič (rapporteur), Leonardo Mazza (directeur de thèse), Grégoire Misguich, Pierre Nataf.