1. Extracting dynamical maps of non-Markovian open quantum systems.
- Author
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Strachan, David J., Purkayastha, Archak, and Clark, Stephen R.
- Subjects
ANDERSON model ,ORTHOGONAL polynomials ,ISOMORPHISM (Mathematics) ,SYSTEM dynamics ,MEMORY ,MARKOV spectrum - 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. First, we use an orthogonal polynomial mapping and thermofield doubling to arrive at a purified chain representation of the baths whose length directly equates to a time over which the dynamics of the infinite baths is faithfully captured. Second, 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 auxiliary 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. These timescales form a hierarchy τ m L ≤ τ m Λ ≤ τ re , where τre is a characteristic relaxation time of the dynamics. Our numerical examples of interacting spinless Fermi chains and the single impurity Anderson model demonstrate regimes where τre ≫ τm , where our approach can offer a significant speedup in determining the stationary state compared to directly simulating the long-time limit. Our results also show that having access to Λ ̂ (τ) affords a number of insightful analyses of the open system thus far not commonly exploited. [ABSTRACT FROM AUTHOR]- Published
- 2024
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