  For open quantum systems,a short-time evolution is usually well described by
the effective non-Hermitian Hamiltonians,while long-time dynamics requires the
Lindblad master equation,in which the Liouvillian superoperators characterize
the time evolution. In this paper, we constructed an open system by adding
suitable gain and loss operators to the Chen insulator to investigate the time
evolution of quantum states at long times by numerical simulations.Finally,we
also propose a topolectrical circuits to realize the dissipative system for
experimental observation. It is found found that the opening and closing of the
Liouvillian gap leads to different damping behaviours of the system and that
the presence of non-Hermitian skin effects leads to a phenomenon of chiral
damping with sharp wavefronts.Our study deepens the understanding of quantum
dynamics of dissipative system.
