Dynamical response and time correlation functions in random quantum systems Article Swipe
Sudhir R. Jain
,
Pierre Gaspard
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2408.09419
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2408.09419
Time-dependent response and correlation functions are studied in random quantum systems composed of infinitely many parts without mutual interaction and defined with statistically independent random matrices. The latter are taken within the three Wigner-Dyson universality classes. In these systems, the response functions are shown to be exactly given by statistical averages over the random-matrix ensemble. Analytical results are obtained for the time dependence of the mean response and correlation functions at zero and positive temperatures. At long times, the mean correlation functions are shown to have a power-law decay for GOE at positive temperatures, but for GUE and GSE at zero temperature. Otherwise, the decay is much faster in time. In relation to these power-law decays, the associated spectral densities have a dip around zero frequency. The diagrammatic method is developed to obtain higher-order response functions and the third-order response function is explicitly calculated. The response to impulsive perturbations is also considered. In addition, the quantum fluctuations of the correlation function in individual members of the ensemble are characterised in terms of their probability distribution, which is shown to change with the temperature.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2408.09419
- https://arxiv.org/pdf/2408.09419
- OA Status
- green
- Cited By
- 1
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4402533213
All OpenAlex metadata
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https://openalex.org/W4402533213Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2408.09419Digital Object Identifier
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Dynamical response and time correlation functions in random quantum systemsWork title
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preprintOpenAlex work type
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-08-18Full publication date if available
- Authors
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Sudhir R. Jain, Pierre GaspardList of authors in order
- Landing page
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https://arxiv.org/abs/2408.09419Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2408.09419Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2408.09419Direct OA link when available
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Statistical physics, Correlation, Quantum, Physics, Mathematics, Computer science, Quantum mechanics, GeometryTop concepts (fields/topics) attached by OpenAlex
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1Total citation count in OpenAlex
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2025: 1Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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