Extracting Dynamical Maps of Non-Markovian Open Quantum Systems

David J. Strachan; Archak Purkayastha; Stephen R. Clark

doi:10.1063/5.0228428

paper

Extracting Dynamical Maps of Non-Markovian Open Quantum Systems

arXiv:2409.17051 · doi:10.1063/5.0228428

Abstract

The most general description of quantum evolution up to a time $τ$ is a completely positive tracing preserving map known as a dynamical map $Λ^(τ)$ . Here we consider $Λ^(τ)$ arising from suddenly coupling a system to one or more thermal baths with a strength that is neither weak nor strong. Given no clear separation of characteristic system/bath time scales $Λ^(τ)$ is generically expected to be non-Markovian, however we do assume the ensuing dynamics has a unique steady state implying the baths possess a finite memory time $τ_{m}$ . By combining several techniques within a tensor network framework we directly and accurately extract $Λ^(τ)$ for a small number of interacting fermionic modes coupled to infinite non-interacting Fermi baths. We employ the Choi-Jamiolkowski isomorphism so that $Λ^(τ)$ can be fully reconstructed from a single pure state calculation of the unitary dynamics of the system, bath and their replica auxillary modes up to time $τ$ . From $Λ^(τ)$ we also compute the time local propagator $L^(τ)$ . By examining the convergence with $τ$ of the instantaneous fixed points of these objects we establish their respective memory times $τ_{m}^{Λ}$ and $τ_{m}^{L}$ . Beyond these times, the propagator $L^(τ)$ and dynamical map $Λ^(τ)$ accurately describe all the subsequent long-time relaxation dynamics up to stationarity. Our numerical examples of interacting spinless Fermi chains and the single impurity Anderson model demonstrate regimes where our approach can offer a significant speedup in determining the stationary state compared to directly simulating the long-time limit.

v2, 12 pages, 10 figures

Extracting Dynamical Maps of Non-Markovian Open Quantum Systems

Abstract

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