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Recent experiments have reported that novel physics emerge in open quantummany-body systems due to an interplay of interactions and dissipation, whichstimulate theoretical studies of the many-body Lindblad equation. Although thestrong dissipation regime receives considerable interest in this context, thiswork focuses on the weak bulk dissipation. By examining the spectral propertyof the many-body Lindblad generator, we find that its spectral gap genericallyshows singularity in the weak dissipation limit when the thermodynamic limit istaken first. Such singular behavior is related to the concept of theRuelle-Pollicott resonance in chaos theory, which determines the timescale ofthermalization of an isolated system. Thus, the many-body Lindblad equation inthe weak dissipation regime contains nontrivial information on intrinsicproperties of a quantum many-body system.

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