Algebraic criteria for complete relaxation in autonomous and periodically driven open quantum systems
Year: 2026
Type: preprint
Abstract: We derive sufficient criteria that guarantee convergence of open quantum system dynamics to a unique long-time state independent of the initial conditions. We refer to this behavior as complete relaxation. Focusing on systems described by Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equations on finite-dimensional Hilbert spaces, our approach uses only elementary mathematical arguments. For autonomous systems, we recover three previously derived relaxation criteria, which can be expressed as algebraic conditions on the Lindblad operators and the Hamiltonian entering the GKSL equation. For periodically driven systems, we obtain a new criterion involving a similar algebraic condition and a local continuity requirement on the time-dependent GKSL generator. This result implies an earlier criterion for complete relaxation formulated in Ref. [J. Phys. A 52, 43LT01 (2019)]. We also discuss implications of our approach for periodically modulated classical master equations, as well as extensions to driven systems without a periodicity constraint.
Source: arXiv (Cornell University)
Authors: Menczel, Paul, Brandner, Kay
Institutions: RIKEN Center for Quantum Computing, University of Nottingham
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: Collective Quantum Thermodynamics, G3580386859, 初期の誤り耐性量子計算に向けた量子シミュレーションと機械学習, G5471319912, Novel non-equilibrium states of matter in periodically driven spin systems: from time crystals to integrated thermal machines, Collective Quantum Thermodynamics: Quantum vs Classical, G7570018266, G8517220141
OpenAlex ID: W7223213807