Hilbert Space Diffusion in Systems with Approximate Symmetries Article Swipe
Rahel L. Baumgartner
,
Luca V. Delacrétaz
,
Pranjal Nayak
,
Julian Sonner
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2405.19260
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2405.19260
Random matrix theory (RMT) universality is the defining property of quantum mechanical chaotic systems, and can be probed by observables like the spectral form factor (SFF). In this paper, we describe systematic deviations from RMT behaviour at intermediate time scales in systems with approximate symmetries. At early times, the symmetries allow us to organize the Hilbert space into approximately decoupled sectors, each of which contributes independently to the SFF. At late times, the SFF transitions into the final ramp of the fully mixed chaotic Hamiltonian. For approximate continuous symmetries, the transitional behaviour is governed by a universal process that we call Hilbert space diffusion. The diffusion constant corresponding to this process is related to the relaxation rate of the associated nearly conserved charge. By implementing a chaotic sigma model for Hilbert-space diffusion, we formulate an analytic theory of this process which agrees quantitatively with our numerical results for different examples.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2405.19260
- https://arxiv.org/pdf/2405.19260
- OA Status
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- Related Works
- 10
- OpenAlex ID
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https://openalex.org/W4399198693Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2405.19260Digital Object Identifier
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Hilbert Space Diffusion in Systems with Approximate SymmetriesWork title
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preprintOpenAlex work type
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enPrimary language
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2024Year of publication
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2024-05-29Full publication date if available
- Authors
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Rahel L. Baumgartner, Luca V. Delacrétaz, Pranjal Nayak, Julian SonnerList of authors in order
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https://arxiv.org/abs/2405.19260Publisher landing page
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https://arxiv.org/pdf/2405.19260Direct link to full text PDF
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2405.19260Direct OA link when available
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Homogeneous space, Hilbert space, Diffusion, Space (punctuation), Mathematics, Pure mathematics, Statistical physics, Mathematical analysis, Physics, Computer science, Geometry, Thermodynamics, Operating systemTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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