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arXiv · 1512.05562

Floquet theorem for open systems and its applications

C. M. Dai·Z. C. Shi·X. X. Yi
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Abstract

For a closed system with periodic driving, Floquet theorem tells that the time evolution operator can be written as $ U(t,0)\equiv P(t)e^{\frac{-i}{\hbar}H_F t}$ with $P(t+T)=P(t)$, and $H_F$ is Hermitian and time-independent called Floquet Hamiltonian. In this work, we extend the Floquet theorem from closed systems to open systems described by a Lindblad master equation that is periodic in time. Lindbladian expansion in powers of $\frac 1 ω$ is derived, where $ω$ is the driving frequency. Two examples are presented to illustrate the theory. We find that appropriate trace preserving time-independent Lindbladian of such a periodically driven system can be constructed by the application of open system Floquet theory, and it agrees well with the exact dynamics in the high frequency limit.

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C. M. Dai, Z. C. Shi, X. X. Yi. 2015-12-17. Floquet theorem for open systems and its applications. https://doi.org/10.1103/physreva.93.032121

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