Extracting Dynamical Maps of Non-Markovian Open Quantum Systems
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912084913029120 |
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| author | Strachan, David J. Purkayastha, Archak Clark, Stephen R. |
| author_facet | Strachan, David J. Purkayastha, Archak Clark, Stephen R. |
| contents | The most general description of quantum evolution up to a time $τ$ is a completely positive tracing preserving map known as a dynamical map $\hatΛ(τ)$. Here we consider $\hatΛ(τ)$ 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 $\hatΛ(τ)$ 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 $τ_{\rm m}$. By combining several techniques within a tensor network framework we directly and accurately extract $\hatΛ(τ)$ for a small number of interacting fermionic modes coupled to infinite non-interacting Fermi baths. We employ the Choi-Jamiolkowski isomorphism so that $\hatΛ(τ)$ 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 $\hatΛ(τ)$ we also compute the time local propagator $\hat{\mathcal{L}}(τ)$. By examining the convergence with $τ$ of the instantaneous fixed points of these objects we establish their respective memory times $τ^Λ_{\rm m}$ and $τ^{\mathcal{L}}_{\rm m}$. Beyond these times, the propagator $\hat{\mathcal{L}}(τ)$ and dynamical map $\hatΛ(τ)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17051 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extracting Dynamical Maps of Non-Markovian Open Quantum Systems Strachan, David J. Purkayastha, Archak Clark, Stephen R. Quantum Physics The most general description of quantum evolution up to a time $τ$ is a completely positive tracing preserving map known as a dynamical map $\hatΛ(τ)$. Here we consider $\hatΛ(τ)$ 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 $\hatΛ(τ)$ 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 $τ_{\rm m}$. By combining several techniques within a tensor network framework we directly and accurately extract $\hatΛ(τ)$ for a small number of interacting fermionic modes coupled to infinite non-interacting Fermi baths. We employ the Choi-Jamiolkowski isomorphism so that $\hatΛ(τ)$ 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 $\hatΛ(τ)$ we also compute the time local propagator $\hat{\mathcal{L}}(τ)$. By examining the convergence with $τ$ of the instantaneous fixed points of these objects we establish their respective memory times $τ^Λ_{\rm m}$ and $τ^{\mathcal{L}}_{\rm m}$. Beyond these times, the propagator $\hat{\mathcal{L}}(τ)$ and dynamical map $\hatΛ(τ)$ 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. |
| title | Extracting Dynamical Maps of Non-Markovian Open Quantum Systems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2409.17051 |