Liouvillian-gap analysis of open quantum many-body systems in the weak dissipation limit

Takashi Mori

Published 2023-11-17Version 1

Recent experiments have reported that novel physics emerge in open quantum many-body systems due to an interplay of interactions and dissipation, which stimulate theoretical studies of the many-body Lindblad equation. Although the strong dissipation regime receives considerable interest in this context, this work focuses on the weak bulk dissipation. By examining the spectral property of the many-body Lindblad generator, we find that its spectral gap generically shows singularity in the weak dissipation limit when the thermodynamic limit is taken first. Such singular behavior is related to the concept of the Ruelle-Pollicott resonance in chaos theory, which determines the timescale of thermalization of an isolated system. Thus, the many-body Lindblad equation in the weak dissipation regime contains nontrivial information on intrinsic properties of a quantum many-body system.