Asymptotic Floquet states of non-Markovian systems

2017/07/31 by Luca Magazzù, Sergey Denisov, Peter Hänggi
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Floquet theory #Markov process #Mathematical analysis #Mathematical physics #Mathematics #Physics #Projection (relational algebra) #Propagator #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum mechanics #Relaxation (psychology) #State (computer science) #State space #Statistical physics #Subspace topology #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreva.96.042103

published as Phys. Rev. A 96, 042103 (2017) · Phys. Rev. A (in press); 6 pages, 2 figures

openalex created_date 2017/07/21 · arxiv created 2017/09/17 · openalex publication_date 2017/10/05 · arxiv updated 2017/10/09 · openalex updated_date 2026/08/05

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 nonphysical---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 quantum random walk model.

Citations

• Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering
• Driven quantum transport on the nanoscale
• Steady States and Quasienergies of a Quantum-Mechanical System in an Oscillating Field
• Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time
• Non-Markovian master equations from piecewise dynamics
• Genuine quantum trajectories for non-Markovian processes
• Memory effects in complex materials and nanoscale systems
• On approximation of functions by exponential sums
• Experimental control of the transition from Markovian to non-Markovian dynamics of open quantum systems
• Generalized Floquet Theory: Application to Dynamical Systems with Memory and Bloch’s Theorem for Nonlocal Potentials
• The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables
• Engineering photonic Floquet Hamiltonians through Fabry–Pérot resonators
• Sur les équations différentielles linéaires à coefficients périodiques
• Fate of a discrete time crystal in an open system
• Quantum Computation and Quantum Information