Slowing down of relaxation processes by Liouvillian skin effect in the open quantum system

Every quantum system that we wish to study is inevitably coupled to some form of environment and hence an open quantum system. The coupling to the environment can for example induce dissipation. A crucial question is what determines the timescale that is called relaxation time for a given system to reach a steady state. For Markovian environments, the system state evolves according to the Lindblad master equation. The relaxation time is then determined by the spectral gap of the Liouville superoperator. However, it is natural to ask whether the relaxation time depends not only on the spectral gap but also on some other properties of the Liouvillian. 

In this talk, I will first quickly review the derivation of the Lindblad master equation[1] and the topic of the non-hermitian skin effect[2]. Then I will introduce the concept called the Liouvillian skin effect and present the slowing down of relaxation processes due to the Liouvillian skin effect[3]. 

[1]H.P. Breuer & F. Petruccione, The Theory of Open Quantum System.
[2]Zhang K, Yang Z, Fang C. Correspondence between winding numbers and skin modes in non-Hermitian systems[J]. Physical Review Letters, 2020, 125(12): 126402.
[3]Haga T, Nakagawa M, Hamazaki R, et al. Liouvillian skin effect: Slowing down of relaxation processes without gap closing[J]. Physical Review Letters, 2021, 127(7): 070402.