Path integral approach to quantum thermalization
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911142403637248 |
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| author | Altland, Alexander Kim, Kun Woo Micklitz, Tobias |
| author_facet | Altland, Alexander Kim, Kun Woo Micklitz, Tobias |
| contents | We introduce a quasiclassical Green function approach describing the unitary yet irreversible dynamics of quantum systems effectively acting as their own environment. Combining a variety of concepts of quantum many-body theory, notably the nonlinear $σ$-model of disordered systems, the $G Σ$-formalism for strong correlations, and real time path integration, the theory is capable of describing a wide range of system classes and disorder models. It extends previous work beyond perturbation theory (in inverse Hilbert space dimensions), enabling a description of thermalization dynamics from short scattering times, through the onset of ergodicity at an effective `Thouless time', up to the many-body Heisenberg time. We illustrate the approach with two case studies, (i) a brickwork model of unitarily coupled quantum circuits with and without conserved symmetries, and (ii) an array of capacitively coupled quantum dots. Using the spectral form factor as a test observable, we find good agreement with numerical simulations. We present our formalism in a self-contained and pedagogical manner, aiming to provide a transferable toolbox for the first-principles description of many-body chaotic quantum systems in regimes of strong entanglement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06028 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Path integral approach to quantum thermalization Altland, Alexander Kim, Kun Woo Micklitz, Tobias Mesoscale and Nanoscale Physics Quantum Physics We introduce a quasiclassical Green function approach describing the unitary yet irreversible dynamics of quantum systems effectively acting as their own environment. Combining a variety of concepts of quantum many-body theory, notably the nonlinear $σ$-model of disordered systems, the $G Σ$-formalism for strong correlations, and real time path integration, the theory is capable of describing a wide range of system classes and disorder models. It extends previous work beyond perturbation theory (in inverse Hilbert space dimensions), enabling a description of thermalization dynamics from short scattering times, through the onset of ergodicity at an effective `Thouless time', up to the many-body Heisenberg time. We illustrate the approach with two case studies, (i) a brickwork model of unitarily coupled quantum circuits with and without conserved symmetries, and (ii) an array of capacitively coupled quantum dots. Using the spectral form factor as a test observable, we find good agreement with numerical simulations. We present our formalism in a self-contained and pedagogical manner, aiming to provide a transferable toolbox for the first-principles description of many-body chaotic quantum systems in regimes of strong entanglement. |
| title | Path integral approach to quantum thermalization |
| topic | Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2509.06028 |