Thermalisation as Diffusion in Hilbert Space
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918384512270336 |
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| author | Lunkin, Aleksey |
| author_facet | Lunkin, Aleksey |
| contents | We develop a microscopic theory of thermalisation for a thermometer coupled to a many-body bath beyond standard Markovian and Fermi-golden-rule assumptions. By modeling interaction matrix elements in the non-interacting basis as independent random variables, we derive a diffusion-propagator expression for the reduced dynamics and show that relaxation is controlled by the distribution of interaction-induced level broadenings. The theory predicts a thermalisation timescale set by the inverse typical broadening and yields a non-Markovian generalization of global balance. Exact-diagonalization tests for heavy-tailed L{é}vy couplings, an all-to-all transverse-field Ising model, and the one-dimensional Imbrie model show good agreement with these predictions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12234 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Thermalisation as Diffusion in Hilbert Space Lunkin, Aleksey Disordered Systems and Neural Networks Statistical Mechanics Quantum Physics We develop a microscopic theory of thermalisation for a thermometer coupled to a many-body bath beyond standard Markovian and Fermi-golden-rule assumptions. By modeling interaction matrix elements in the non-interacting basis as independent random variables, we derive a diffusion-propagator expression for the reduced dynamics and show that relaxation is controlled by the distribution of interaction-induced level broadenings. The theory predicts a thermalisation timescale set by the inverse typical broadening and yields a non-Markovian generalization of global balance. Exact-diagonalization tests for heavy-tailed L{é}vy couplings, an all-to-all transverse-field Ising model, and the one-dimensional Imbrie model show good agreement with these predictions. |
| title | Thermalisation as Diffusion in Hilbert Space |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2603.12234 |