1. One-dimensional Monte Carlo dynamics at zero temperature
- Author
-
Alexei D. Chepelianskii, Emmanuel Trizac, Hendrik Schawe, Satya N. Majumdar, Alexei, Chepelianskii, Laboratoire de Physique des Solides (LPS), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Laboratoire de Physique Théorique et Modélisation (LPTM - UMR 8089), and Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY)
- Subjects
Statistics and Probability ,Physics ,Work (thermodynamics) ,Statistical Mechanics (cond-mat.stat-mech) ,05 social sciences ,Monte Carlo method ,050301 education ,General Physics and Astronomy ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Probability density function ,Potential energy ,[PHYS.COND.CM-MSQHE] Physics [physics]/Condensed Matter [cond-mat]/Mesoscopic Systems and Quantum Hall Effect [cond-mat.mes-hall] ,Discrete time and continuous time ,Random walker algorithm ,Modeling and Simulation ,0502 economics and business ,Jump ,Statistical physics ,0503 education ,Scaling ,050203 business & management ,Mathematical Physics ,[PHYS.COND.CM-MSQHE]Physics [physics]/Condensed Matter [cond-mat]/Mesoscopic Systems and Quantum Hall Effect [cond-mat.mes-hall] ,Condensed Matter - Statistical Mechanics - Abstract
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., J. Phys. A: Math. Theor (2021)
- Published
- 2021