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Title: Langevin synchronization in a time-dependent, harmonic basin: An exact solution in 1D

Abstract

The trajectories of two particles undergoing Langevin dynamics while sharing a common noise sequence can merge into a single (master) trajectory. In this paper, we present an exact solution for a particle undergoing Langevin dynamics in a harmonic, time-dependent potential, thus extending the idea of synchronization to nonequilibrium systems. We calculate the synchronization level, i.e., the mismatch between two trajectories sharing a common noise sequence, in the underdamped, critically damped, and overdamped regimes. In conclusion, we provide asymptotic expansions in various limiting cases and compare to the time independent case.

Authors:
 [1];  [2]
  1. Federal Univ. of Bahia, Salvador (Brazil). Inst. of Physics
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Federal Univ. of Bahia, Salvador (Brazil)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); USDOE National Nuclear Security Administration (NNSA); Foundation for Science and Technology (FCT) (Portugal); Calouste Gulbenkian Foundation (Portugal)
OSTI Identifier:
1463502
Alternate Identifier(s):
OSTI ID: 1422660
Report Number(s):
LA-UR-18-21972
Journal ID: ISSN 0021-9606
Grant/Contract Number:  
AC52-06NA25396; SFRH/BPD/34375/2007
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 148; Journal Issue: 8; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; oscillators; thermal instruments; elasticity; thermodynamics; electronic devices; numerical modeling; friction; chemical compounds

Citation Formats

Cadilhe, A., and Voter, Arthur F. Langevin synchronization in a time-dependent, harmonic basin: An exact solution in 1D. United States: N. p., 2018. Web. doi:10.1063/1.5016632.
Cadilhe, A., & Voter, Arthur F. Langevin synchronization in a time-dependent, harmonic basin: An exact solution in 1D. United States. doi:10.1063/1.5016632.
Cadilhe, A., and Voter, Arthur F. Mon . "Langevin synchronization in a time-dependent, harmonic basin: An exact solution in 1D". United States. doi:10.1063/1.5016632. https://www.osti.gov/servlets/purl/1463502.
@article{osti_1463502,
title = {Langevin synchronization in a time-dependent, harmonic basin: An exact solution in 1D},
author = {Cadilhe, A. and Voter, Arthur F.},
abstractNote = {The trajectories of two particles undergoing Langevin dynamics while sharing a common noise sequence can merge into a single (master) trajectory. In this paper, we present an exact solution for a particle undergoing Langevin dynamics in a harmonic, time-dependent potential, thus extending the idea of synchronization to nonequilibrium systems. We calculate the synchronization level, i.e., the mismatch between two trajectories sharing a common noise sequence, in the underdamped, critically damped, and overdamped regimes. In conclusion, we provide asymptotic expansions in various limiting cases and compare to the time independent case.},
doi = {10.1063/1.5016632},
journal = {Journal of Chemical Physics},
number = 8,
volume = 148,
place = {United States},
year = {2018},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Figures / Tables:

FIG. 1 FIG. 1: Schematic of pairs of trajectories merging into a master trajectory for the (a) time-independent and (b) time-dependent potentials. The vertical (blue) lines represent guides indicative of the typical bounds for a trajectory evolving in the basin at a given temperature, T. The synchronization level is computed as themore » driven system crosses ω0 at time t, where the two potentials become equivalent, i.e., they possess the same curvature.« less

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