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Exploring a new class of non-Markovian dynamical landscape through the lens of floquet stroboscopic divisibility

In open quantum system study, it is commonly accepted notion that Markovian dynamic, which does not depend on past history, exhibits a completely positive (CP) divisible dynamical map while non-Markovian one, depending on the entire past history, evolves under non-CP divisible dynamical map. In this talk, we provide a general description of a time-local master equation for a system coupled to a non-Markovian reservoir based on the Floquet theory. This allows us to have a divisible dynamical map at discrete times, which we refer to as Floquet stroboscopic divisibility (FSD). We illustrate the theory by considering a quantum harmonic oscillator coupled to both non-Markovian and Markovian baths. Our findings provide us with a theory for the exact calculation of spectral properties of time-local non-Markovian Liouvillian operators. If time permits, application of FSD to dynamical quantum phase transition will be highlighted.