One-dimensional Monte Carlo dynamics at zero temperature - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

One-dimensional Monte Carlo dynamics at zero temperature

Résumé

We investigate, both analytically and with numerical simulations, a Monte Carlo dynamics at zero temperature, where a random walker evolving in continuous space and discrete time seeks to minimize its potential energy, by decreasing this quantity at each jump. The resulting dynamics is universal in the sense that it does not depend on the underlying potential energy landscape, as long as it admits a unique minimum; furthermore, the long time regime does not depend on the details of the jump distribution, but only on its behaviour for small jumps. We work out the scaling properties of this dynamics, as embodied by the walker probability density. Our analytical predictions are in excellent agreement with direct Monte Carlo simulations.

Dates et versions

hal-03435831 , version 1 (18-11-2021)

Identifiants

Citer

Alexei D. Chepelianskii, Satya N. Majumdar, Hendrik Schawe, Emmanuel Trizac. One-dimensional Monte Carlo dynamics at zero temperature. 2021. ⟨hal-03435831⟩
23 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More