2018/03/31 by Stefano Scopa, Gabriel T. Landi, Dragi Karevski
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Carnot cycle #Classical mechanics #Floquet theory #Harmonic oscillator #Limit (mathematics) #Limit cycle #Lindblad equation #Master equation #Mathematical analysis #Mathematics #Nonlinear system #Physics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Thermal Radiation and Cooling Technologies #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physreva.97.062121
published as Phys. Rev. A 97, 062121 (2018)
openalex created_date 2018/04/06 · arxiv created 2018/06/06 · openalex publication_date 2018/06/20 · arxiv updated 2018/06/27 · openalex updated_date 2026/08/06
The operation of autonomous finite-time quantum heat engines relies on the existence of a stable limit cycle in which the dynamics becomes periodic. The two main questions that naturally arise are therefore whether such a limit cycle will eventually be reached and, once it has, what the state of the system is within the limit cycle. In this paper we show that the application of Floquet's theory to Lindblad dynamics offers clear answers to both questions. By moving to a generalized rotating frame, we show that it is possible to identify a single object, the Floquet Liouvillian, which encompasses all operating properties of the engine. First, its spectrum dictates the convergence to a limit cycle. Second, the state within the limit cycle is precisely its zero eigenstate, therefore reducing the problem to that of determining the steady state of a time-independent master equation. To illustrate the usefulness of this theory, we apply it to a harmonic oscillator subject to a time-periodic work protocol and time-periodic dissipation, an open-system generalization of the Ermakov-Lewis theory. The use of this theory to implement a finite-time Carnot engine subject to continuous frequency modulations is also discussed.