Floquet stroboscopic divisibility in non-Markovian dynamics

Abstract

We provide a general description of a time-local master equation for a system coupled to a non-Markovian reservoir based on Floquet theory. This allows us to have a divisible dynamical map at discrete times, which we refer to as Floquet stroboscopic divisibility. We illustrate the theory by considering a 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, and might shed light on the nature and existence of the steady state in non-Markovian dynamics.

Asymptotic Floquet states of a periodically driven spin-boson system in the nonperturbative coupling regime

“…While this GME for the spin dynamics cannot be evaluated within the standard Floquet formalism (because of the time-nonlocal character of the dynamics), the evolution of the spin-boson system in the full Hilbert space is governed by a time-periodic Hamiltonian and, therefore, can be -though only formally -handled with the standard Floquet theory. The Floquet theory also applies to the reduced dynamics when the description can be given in terms of time-local evolution equations, typically in the weak coupling regime, thus resulting in the Bloch-Redfield or Lindblad master equations [43][44][45][46][47]. In the limit of a high frequency driving, the Floquet approach can also be implemented beyond the weak coupling limit [48], by using the inverse frequency of modulations as a perturabtion parameter.…”

Dynamical quantum phase transitions and non-Markovian dynamics

“…As we have mentioned earlier, DQPT is observed when a quantum system undergoes a sudden quench across equilibrium critical point. In order to apply the minimization principle [26,27] within the open quantum systems framework of Floquet stroboscopic divisibility that we proposed in a recent paper [49] (see Appendix B), we treat the Ising chain A as a drain and B as a current source, which will be clarified below. < l a t e x i t s h a 1 _ b a s e 6 4 = " i J…”

“…See Appendix B and Ref. [49] for a detailed explanation of our open quantum system theory. On important aspect In this simulation we have used the same interspin coupling, transverse magnetic field, and number of bosonic modes as in Fig.…”

“…of the master equation is that due to the time-periodic character of the rates, the dynamics of the Ising ring is divisible at stroboscopic times, which is referred to as Floquet stroboscopic divisibility [49].…”

“…In particular, we consider quenches in the context of open quantum systems that are described by Lindblad-type master equations. Furthermore, we investigate the effect of non-Markovian environments [49] on signatures of DQPTs experienced by an Ising chain. We show that signatures of DQPT are robust under the action of both Markovian and non-Markovian dephasing channels; no matter how strongly they couple to the quantum system.…”