On the Lyapunov-Perron reducible Markovian Master Equation

2020/12/31 by Krzysztof Szczygielski
Mathematics · Physics and Astronomy · #Applied mathematics #Hamiltonian (control theory) #Hamiltonian system #Limit (mathematics) #Lyapunov function #Markov process #Master equation #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Nonlinear system #Operator (biology) #Physics #Quantum #Quantum chaos and dynamical systems #Quantum many-body systems #Quantum mechanics #Quasiperiodic function #Schrödinger equation #Schrödinger's cat #Spectral Theory in Mathematical Physics #Statistical physics #math-ph #math.MP #msc:34G10 #msc:42A99 #msc:47B65 #msc:60J25 #quant-ph

paper · pdf · doi:10.1142/s0129055x22500040

published as Reviews in Mathematical Physics 34(02) 2250004 (2022) · Final version. 22 pages, no figures

openalex publication_date 2021/09/29 · arxiv created 2022/02/28 · arxiv updated 2022/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider an open quantum system in M_d(ℂ) governed by quasiperiodic Hamiltonian with rationally independent frequencies and under assumption of Lyapunov-Perron reducibility of associated Schroedinger equation. We construct the Markovian Master Equation and resulting CP-divisible evolution in weak coupling limit regime, generalizing our previous results from periodic case. The analysis is conducted with application of projection operator techniques and concluded with some results regarding stability of solutions and existence of quasiperiodic global steady state.

Citations

• Internal consistency of fault-tolerant quantum error correction in light of rigorous derivations of the quantum Markovian limit
• Completely positive dynamical semigroups of N-level systems
• On the application of Floquet theorem in development of time-dependent Lindbladians
• Open Quantum Systems. An Introduction