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.

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

References in corpus (30)

• Floquet Topological Insulator in Semiconductor Quantum Wells
• Non-Markovian dynamics in open quantum systems
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Atomic quantum gases in periodically driven optical lattices
• Observation of a Discrete Time Crystal
• Observation of discrete time-crystalline order in a disordered dipolar many-body system
• Floquet Time Crystals
• Memory Metamaterials
• Memory effects in complex materials and nanoscale systems
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Driven quantum transport on the nanoscale
• High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective
• Quantum simulation of frustrated magnetism in triangular optical lattices
• Experimental control of the transition from Markovian to non-Markovian dynamics of open quantum systems
• Floquet engineering of correlated tunneling in the Bose-Hubbard model with ultracold atoms
• Genuine quantum trajectories for non-Markovian processes
• Quantum Semi-Markov Processes
• Collision model for non-Markovian quantum dynamics
• Stochastic Representation of a Class of Non-Markovian Completely Positive Evolutions
• Generalized Bose-Einstein condensation into multiple states in driven-dissipative systems
• Markovian embedding of non-Markovian superdiffusion
• The fate of a discrete time crystal in an open system
• Asymptotic Floquet states of open quantum systems: The role of interaction
• Kondo memory in driven strongly-correlated quantum dots
• Generalized master equations leading to completely positive dynamics
• Non-Markovian master equations from piecewise dynamics
• A classical appraisal of quantum definitions of non-Markovian dynamics
• Generalized Floquet theory: application to dynamical systems with memory and Bloch's theorem for nonlocal potentials
• Markovian embedding of non-Markovian quantum collisional models
• Engineering Photonic Floquet Hamiltonians through Fabry Pérot Resonators

Cited by in corpus (8)

• Floquet states in dissipative open quantum systems
• Asymptotic Floquet states of a periodically driven spin-boson system in the nonperturbative coupling regime
• Minimal quantum thermal machine in a bandgap environment: non-Markovian features and anti-Zeno advantage
• Floquet stroboscopic divisibility in non-Markovian dynamics
• Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method
• Mode attraction in Floquet systems with memory: application to magnonics
• About the performance of perturbative treatments of the spin-boson dynamics within the hierarchical equations of motion approach
• Dissipative features of the driven spin-fermion system