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Relaxation speed in quenched-random force fields — arXiv:2610.41991

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.41991
License (as archived): CC0-1.0
Archived: 2026-11-02T08:10:03.129Z
SHA-256 of the archived text: bd16f88e01bd3c9f644977f9c3a4b3edd7bb60847c83796e85a5f2f1a31e9641
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How to cite

Relaxation speed in quenched-random force fields — arXiv:2610.41991 — arXiv (en), https://arxiv.org/abs/2610.41991 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_009df5efb2ab (Metraipolis archive dc_009df5efb2ab, sha256 bd16f88e01bd3c9f644977f9c3a4b3edd7bb60847c83796e85a5f2f1a31e9641)

BibTeX

@misc{dc009df5efb2ab,
  title = {Relaxation speed in quenched-random force fields — arXiv:2610.41991},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.41991},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_009df5efb2ab; sha256 bd16f88e01bd3c9f644977f9c3a4b3edd7bb60847c83796e85a5f2f1a31e9641},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.41991. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Disorder is commonly expected to slow down relaxation, as in glasses and disordered magnets. Here we show that this need not be the case in general, by analysing the asymptotic relaxation rate of a Brownian particle in a harmonic background potential and a quenched-random Gaussian force field with conservative and non-conservative components. Combining weak-disorder perturbation theory, random-matrix theory, and numerical solutions of the Fokker-Planck equation, we show that the outcome depends on the geometry of the background and on the properties of the random forces. We identify two distinct mechanisms that shape the relaxation speed: an effective stiffening of the background by the disorder, as previously reported in one dimension, and interactions (repulsive and attractive) between the levels of the Fokker-Planck operator. Through level attraction, a common feature of non-Hermitian operators, non-conservative driving forces pull the slowest mode towards faster ones, which facilitates faster relaxation. In anisotropic backgrounds, both effects occur at second order in the disorder strength, enabling either slower or faster relaxation. In isotropic backgrounds, level interactions dominate and the disorder affects the degenerate slowest mode already at first order. The shift is then given by the left-most eigenvalue of a Gaussian random matrix and relaxation is generically slowed down. In backgrounds whose anisotropy is comparable to the disorder strength, level attraction is most effective by merging the slowest mode with its neighbour into an oscillating complex-conjugate pair. In this case, relaxation becomes faster on average once the random forces are sufficiently non-conservative. Our results draw a nuanced picture of how disorder affects the asymptotic relaxation speed in complex systems and uncover general mechanisms that are likely to apply beyond the current setting.

Tema degli esploratori: fisica e astronomia (elenco arXiv cond-mat.stat-mech, nuovi lavori del giorno).
Categorie arXiv: Statistical Mechanics (cond-mat.stat-mech) ; Disordered Systems and Neural Networks (cond-mat.dis-nn).
Pagina del lavoro: https://arxiv.org/abs/2610.41991 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-02T07:47:15.688Z dalla pagina https://arxiv.org/list/cond-mat.stat-mech/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).