Thermalisation as Diffusion in Hilbert Space

• URL: http://arxiv.org/abs/2603.12234v1
• Date: Thu, 12 Mar 2026 17:52:15 GMT
• Title: Thermalisation as Diffusion in Hilbert Space
• Abstract summary: We develop a microscopic theory of thermalisation for a thermometer coupled to a many-body bath.<n>By modeling interaction matrix elements as independent random variables, we derive a diffusion-propagator expression for the reduced dynamics.<n>The theory predicts a thermalisation timescale set by the inverse typical broadening and yields a non-Markovian generalization of global balance.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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