Paper
Thermalisation as Diffusion in Hilbert Space
Authors
Aleksey Lunkin
Abstract
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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.12234v1</id>\n <title>Thermalisation as Diffusion in Hilbert Space</title>\n <updated>2026-03-12T17:52:15Z</updated>\n <link href='https://arxiv.org/abs/2603.12234v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.12234v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cond-mat.dis-nn'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cond-mat.stat-mech'/>\n <category scheme='http://arxiv.org/schemas/atom' term='quant-ph'/>\n <published>2026-03-12T17:52:15Z</published>\n <arxiv:comment>14 pages, 5 figures</arxiv:comment>\n <arxiv:primary_category term='cond-mat.dis-nn'/>\n <author>\n <name>Aleksey Lunkin</name>\n </author>\n </entry>"
}