Open quantum system,coupled with an external bath is a key research field of quantum physics.Steady state is the state in which any initial state converges after a long time and is usually of the most interest.However,relatively speaking,the nonequilibrium dynamical processes of quantum many-body systems have been rarely studied.This is mainly due to the fact that quantum many-body systems generally have interactions,and the Hilbert space required for a complete description of their dynamical processes will grow exponentially with the number of particles increasing,and the computational difficulty will increase dramatically as well.Hence,it is a difficult problem to completely describe their dynamical processes completely.With the development of quantum technologies,the interest in the nonequilibrium dynamics of open quantum many-body systems is aroused.A common phenomenon is the metastable state,where the system initially relaxes into a long-lived state and then converges to the final stationary state for a longer time.In this paper,we establish a low-dimensional approximation to describe the metastability dynamics in Markovian open quantum system,based on the spectra of the Liouvillian super-operator.The separation of time scales implies a splitting in the spectrum,and this spectral division allows us to eliminate the fast decay modes by using the perturbation method,and then we establish the effective description in the low-lying eigenmodes subspace.Furthermore,we study the dynamics process of the Rydberg atomic system under electromagnetically induced transparency(EIT)conditions and find that the system can handle metastable dynamics if the atomic interactions are considered.We compare the effective dynamics in the subspace with the actual dynamics in the full space,and the results show that the effective dynamics works well on condition that the perturbation approximation holds.Our work provides a feasible idea and method for establishing an effective and simplified description of the dynamical process of open quantum many-body systems.
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