Asymptotic Floquet states of non-Markovian systems

Abstract

We propose a method to find asymptotic states of a class of periodically modulated open systems which are outside the range of validity of the Floquet theory due to the presence of memory effects. The method is based on a Floquet treatment of the time-local, memoryless dynamics taking place in a minimally enlarged state space where the original system is coupled to auxiliary -- typically non-physical -- variables. A projection of the Floquet solution into the physical subspace returns the sought asymptotic state of the system. The spectral gap of the Floquet propagator acting in the enlarged state space can be used to estimate the relaxation time. We illustrate the method with a modulated version of quantum random walk model.

Phys. Rev. A (in press); 6 pages, 2 figures

References in corpus (7)

• Memory effects in complex materials and nanoscale systems
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Driven quantum transport on the nanoscale
• Genuine quantum trajectories for non-Markovian processes
• Quantum Semi-Markov Processes
• Stochastic Representation of a Class of Non-Markovian Completely Positive Evolutions
• Generalized master equations leading to completely positive dynamics