2019/05/31 by Lucas Sá, Pedro Ribeiro, Tomaž Prosen · 58 citations
Computer Science · Mathematics · Physics and Astronomy · #Dissipation #Dissipative system #Markov process #Quantum Information and Cryptography #Quantum chaos and dynamical systems #Quantum many-body systems #Random matrix #Scaling #Spectral density #Spectral power distribution #Spectral properties #Stochastic process #cond-mat.mes-hall #cond-mat.stat-mech #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8121/ab9337
published in Journal of Physics A Mathematical and Theoretical 53(30), 305303 (Institute of Physics) · 21 pages, 11 figures. v2: minor corrections. v3: additional details, as published
openalex created_date 2019/05/09 · openalex publication_date 2020/05/14 · arxiv created 2020/07/10 · arxiv updated 2020/08/07 · openalex updated_date 2026/08/05
Abstract We study generic open quantum systems with Markovian dissipation, focusing on a class of stochastic Liouvillian operators of Lindblad form with independent random dissipation channels (jump operators) and a random Hamiltonian. We establish that the global spectral features, the spectral gap, and the steady-state properties follow three different regimes as a function of the dissipation strength, whose boundaries depend on the particular quantity. Within each regime, we determine the scaling exponents with the dissipation strength and system size. We find that, for two or more dissipation channels, the spectral gap increases with the system size. The spectral distribution of the steady state is Poissonian at low dissipation strength and conforms to that of a random matrix once the dissipation is sufficiently strong. Our results can help to understand the long-time dynamics and steady-state properties of generic dissipative systems.