Limit cycles in periodically driven open quantum systems

Abstract

We investigate the long-time behavior of quantum N-level systems that are coupled to a Markovian environment and subject to periodic driving. As our main result, we obtain a general algebraic condition ensuring that all solutions of a periodic quantum master equation with Lindblad form approach a unique limit cycle. Quite intuitively, this criterion requires that the dissipative terms of the master equation connect all subspaces of the system Hilbert space during an arbitrarily small fraction of the cycle time. Our results provide a natural extension of Spohn's algebraic condition for the approach to equilibrium to systems with external driving.

9 pages, 1 figure

References in corpus (15)

• Non-Markovian dynamics in open quantum systems
• Quantum Thermodynamics
• The role of quantum information in thermodynamics --- a topical review
• Open Quantum Systems. An Introduction
• Quantum Thermodynamics
• Fundamental aspects of steady-state conversion of heat to work at the nanoscale
• The quantum harmonic Otto cycle
• Discrete Time-Crystalline Order in Cavity and Circuit QED Systems
• Stabilizing Open Quantum Systems by Markovian Reservoir Engineering
• Discrete time crystals in the absence of manifest symmetries or disorder in open quantum systems
• Characteristics of the Limit Cycle of a Reciprocating Quantum Heat Engine
• Geometry and response of Lindbladians
• Periodic Thermodynamics of Open Quantum Systems
• Markovianity criteria for quantum evolution
• Lindblad-Floquet description of finite-time quantum heat engines

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