On the application of Floquet theorem in development of time-dependent Lindbladians

2014/03/31 by Krzysztof Szczygielski · 3 citations
Mathematics · Physics and Astronomy · #Development (topology) #Dynamical systems theory #Floquet theory #Hamiltonian (control theory) #Hamiltonian system #Markov process #Quantum #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #TRACE (psycholinguistics) #advanced mathematical theories #math-ph #math.MP #msc:81S22 #quant-ph

paper · pdf · doi:10.1063/1.4891401

published as J. Math. Phys. 55, 083506 (2014) · 21 pages, no figures; final version added

openalex publication_date 2014/07/31 · arxiv created 2014/08/05 · arxiv updated 2014/08/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In this paper, the mathematical framework providing a description of completely positive and trace preserving dynamics of open quantum systems is addressed. Special case of time-dependent Lindbladian governed by periodic Hamiltonian is concerned. It is proven that appropriate trace preserving dynamical map of such periodically driven system may be constructed by application of Floquet theory. Appropriate Lindbladian and Markovian master equation in weak coupling regime and resulting dynamical map are constructed. Some examples of application of developed technique are given.

Citations

• Quantum refrigerators and the third law of thermodynamics
• 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

Cited by

• Non-equilibrium quantum heat machines
• Amplitude tuning of steady-state entanglement in strongly driven coupled qubits
• On the Lyapunov-Perron reducible Markovian Master Equation