Periodically Driven Open Quantum Systems: Spectral Properties and Non-Equilibrium Steady States

• URL: http://arxiv.org/abs/2401.00131v3
• Date: Mon, 15 Apr 2024 01:28:21 GMT
• Title: Periodically Driven Open Quantum Systems: Spectral Properties and Non-Equilibrium Steady States
• Authors: Hao Chen, Yu-Min Hu, Wucheng Zhang, Michael Alexander Kurniawan, Yuelin Shao, Xueqi Chen, Abhinav Prem, Xi Dai,
• Abstract summary: We discuss Lindblad master equations in the presence of a coherent, time-periodic driving. We prove that any physical system described by a Floquet-Lindblad equation must have at least one textitphysical non-equilibrium steady state.
• Score: 3.319719042621334
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: In this article, we investigate periodically driven open quantum systems within the framework of Floquet-Lindblad master equations. Specifically, we discuss Lindblad master equations in the presence of a coherent, time-periodic driving and establish their general spectral features. We also clarify the notions of transient and non-decaying solutions from this spectral perspective, and then prove that any physical system described by a Floquet-Lindblad equation must have at least one \textit{physical} non-equilibrium steady state (NESS), corresponding to an eigenoperator of the Floquet-Lindblad evolution superoperator $\mathcal{U}_F$ with unit eigenvalue. Since the Floquet-Lindblad formalism encapsulates the entire information regarding the NESS, it in principle enables us to obtain non-linear effects to all orders at once. The Floquet-Lindblad formalism thus provides a powerful tool for studying driven-dissipative solid-state systems, which we illustrate by deriving the nonlinear optical response of a simple two-band model of an insulating solid and comparing it with prior results established through Keldysh techniques.

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