Langevin synchronization in a timedependent, 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, timedependent 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:

 Federal Univ. of Bahia, Salvador (Brazil). Inst. of Physics
 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) (SC22); 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):
 LAUR1821972
Journal ID: ISSN 00219606
 Grant/Contract Number:
 AC5206NA25396; 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 00219606
 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 timedependent, 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 timedependent, 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 timedependent, 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 timedependent, 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, timedependent 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}
}
Other availability
Figures / Tables:
FIG. 1: Schematic of pairs of trajectories merging into a master trajectory for the (a) timeindependent and (b) timedependent 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 »
All figures and tables
(2 total)
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
The simulation of random processes on digital computers: Unavoidable order
journal, March 1983
 Erber, T.; Rynne, T. M.; Darsow, W. F.
 Journal of Computational Physics, Vol. 49, Issue 3
Chaos, noise, and synchronization
journal, March 1994
 Maritan, Amos; Banavar, Jayanth R.
 Physical Review Letters, Vol. 72, Issue 10
Nonlocality of relaxation rates in disordered landscapes
journal, February 2017
 Li, Yunyun; Debnath, Debajyoti; Ghosh, Pulak K.
 The Journal of Chemical Physics, Vol. 146, Issue 8
A possible classification of nonequilibrium steady states
journal, May 2006
 Zia, R. K. P.; Schmittmann, B.
 Journal of Physics A: Mathematical and General, Vol. 39, Issue 24
Exact Solution of an Irreversible OneDimensional Model with Fully Biased spin Exchanges
journal, November 1996
 Cadilhe, AntÓNio M. R.; Privman, Vladimir
 International Journal of Modern Physics B, Vol. 10, Issue 25
Bad Seeds Sprout Perilous Dynamics: Stochastic Thermostat Induced Trajectory Synchronization in Biomolecules
journal, April 2009
 Sindhikara, Daniel J.; Kim, Seonah; Voter, Arthur F.
 Journal of Chemical Theory and Computation, Vol. 5, Issue 6
Transition from chaotic to nonchaotic behavior in randomly driven systems
journal, August 1992
 Fahy, S.; Hamann, D. R.
 Physical Review Letters, Vol. 69, Issue 5
Recycled noise rectification: An automated Maxwell’s daemon
journal, September 2006
 Borromeo, M.; Giusepponi, S.; Marchesoni, F.
 Physical Review E, Vol. 74, Issue 3
Control coherence resonance by noise recycling
journal, February 2009
 Ma, J.; Hou, Z. H.; Xin, H. W.
 The European Physical Journal B, Vol. 69, Issue 1
Locally disrupted synchronization in Langevin molecular dynamics
journal, August 2012
 Georgescu, Andreea I.; Denny, Samuel J.; Joly, Emilien
 Physical Review E, Vol. 86, Issue 2
Stochastic resonance
journal, January 1998
 Gammaitoni, Luca; Hänggi, Peter; Jung, Peter
 Reviews of Modern Physics, Vol. 70, Issue 1
The parallel replica dynamics method – Coming of age
journal, April 2015
 Perez, Danny; Uberuaga, Blas P.; Voter, Arthur F.
 Computational Materials Science, Vol. 100
Parallel replica dynamics for driven systems: Derivation and application to strained nanotubes
journal, January 2007
 Uberuaga, Blas Pedro; Stuart, Steven J.; Voter, Arthur F.
 Physical Review B, Vol. 75, Issue 1
Stochastic synchronization via noise recycling
journal, April 2007
 Borromeo, Marcello; Marchesoni, Fabio
 Physical Review E, Vol. 75, Issue 4
Synchronization induced by Langevin dynamics
journal, May 2001
 Cies̀la, M.; Dias, S. P.; Longa, L.
 Physical Review E, Vol. 63, Issue 6
Synchronization of trajectories in canonical moleculardynamics simulations: Observation, explanation, and exploitation
journal, April 2004
 Uberuaga, Blas P.; Anghel, Marian; Voter, Arthur F.
 The Journal of Chemical Physics, Vol. 120, Issue 14
Molecular dynamics simulations at constant pressure and/or temperature
journal, February 1980
 Andersen, Hans C.
 The Journal of Chemical Physics, Vol. 72, Issue 4
Roundoffinduced coalescence of chaotic trajectories
journal, September 1996
 Longa, Lech; Curado, Evaldo M. F.; Oliveira, Fernando A.
 Physical Review E, Vol. 54, Issue 3
Figures/Tables have been extracted from DOEfunded journal article accepted manuscripts.