Ergodicity of a single particle confined in a nanopore

S. Bernardi, Jesper Schmidt Hansen, F. Frascolli, Billy Todd, Carl Dettmann

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

We analyze the dynamics of a gas particle moving through a nanopore of adjustable width with particular emphasis on ergodicity. We give a measure of the portion of phase space that is characterized by quasiperiodic trajectories which break ergodicity. The interactions between particle and wall atoms are mediated by a Lennard-Jones potential, so that an analytical treatment of the dynamics is not feasible, but making the system more physically realistic. In view of recent studies, which proved non-ergodicity for systems with scatterers interacting via smooth potentials, we find that the non-ergodic component of the
phase space for energy levels typical of experiments, is surprisingly small, i.e. we conclude that the ergodic hypothesis is a reasonable approximation even for a single particle trapped in a nanopore. Due to the numerical scope of this work, our focus will be the onset of ergodic behavior which is evident on time scales accessible to simulations and experimental observations rather than ergodicity in the infinite time limit.
Original languageEnglish
JournalJournal of Statistical Physics
Volume148
Issue number6
Pages (from-to)1156-1169
ISSN0022-4715
Publication statusPublished - 2012

Keywords

  • Ergodic theory
  • Statistical mechanics
  • Dynamical systems
  • Lyapunov exponents

Cite this

Bernardi, S., Hansen, J. S., Frascolli, F., Todd, B., & Dettmann, C. (2012). Ergodicity of a single particle confined in a nanopore. Journal of Statistical Physics, 148(6), 1156-1169.
Bernardi, S. ; Hansen, Jesper Schmidt ; Frascolli, F. ; Todd, Billy ; Dettmann, Carl. / Ergodicity of a single particle confined in a nanopore. In: Journal of Statistical Physics. 2012 ; Vol. 148, No. 6. pp. 1156-1169.
@article{8fc8899f5f3e43ca8cdf4a9a00ecf48c,
title = "Ergodicity of a single particle confined in a nanopore",
abstract = "We analyze the dynamics of a gas particle moving through a nanopore of adjustable width with particular emphasis on ergodicity. We give a measure of the portion of phase space that is characterized by quasiperiodic trajectories which break ergodicity. The interactions between particle and wall atoms are mediated by a Lennard-Jones potential, so that an analytical treatment of the dynamics is not feasible, but making the system more physically realistic. In view of recent studies, which proved non-ergodicity for systems with scatterers interacting via smooth potentials, we find that the non-ergodic component of thephase space for energy levels typical of experiments, is surprisingly small, i.e. we conclude that the ergodic hypothesis is a reasonable approximation even for a single particle trapped in a nanopore. Due to the numerical scope of this work, our focus will be the onset of ergodic behavior which is evident on time scales accessible to simulations and experimental observations rather than ergodicity in the infinite time limit.",
keywords = "Ergodic theory, Statistical mechanics, Dynamical systems, Lyapunov exponents",
author = "S. Bernardi and Hansen, {Jesper Schmidt} and F. Frascolli and Billy Todd and Carl Dettmann",
year = "2012",
language = "English",
volume = "148",
pages = "1156--1169",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York LLC",
number = "6",

}

Bernardi, S, Hansen, JS, Frascolli, F, Todd, B & Dettmann, C 2012, 'Ergodicity of a single particle confined in a nanopore', Journal of Statistical Physics, vol. 148, no. 6, pp. 1156-1169.

Ergodicity of a single particle confined in a nanopore. / Bernardi, S.; Hansen, Jesper Schmidt; Frascolli, F.; Todd, Billy; Dettmann, Carl.

In: Journal of Statistical Physics, Vol. 148, No. 6, 2012, p. 1156-1169.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Ergodicity of a single particle confined in a nanopore

AU - Bernardi, S.

AU - Hansen, Jesper Schmidt

AU - Frascolli, F.

AU - Todd, Billy

AU - Dettmann, Carl

PY - 2012

Y1 - 2012

N2 - We analyze the dynamics of a gas particle moving through a nanopore of adjustable width with particular emphasis on ergodicity. We give a measure of the portion of phase space that is characterized by quasiperiodic trajectories which break ergodicity. The interactions between particle and wall atoms are mediated by a Lennard-Jones potential, so that an analytical treatment of the dynamics is not feasible, but making the system more physically realistic. In view of recent studies, which proved non-ergodicity for systems with scatterers interacting via smooth potentials, we find that the non-ergodic component of thephase space for energy levels typical of experiments, is surprisingly small, i.e. we conclude that the ergodic hypothesis is a reasonable approximation even for a single particle trapped in a nanopore. Due to the numerical scope of this work, our focus will be the onset of ergodic behavior which is evident on time scales accessible to simulations and experimental observations rather than ergodicity in the infinite time limit.

AB - We analyze the dynamics of a gas particle moving through a nanopore of adjustable width with particular emphasis on ergodicity. We give a measure of the portion of phase space that is characterized by quasiperiodic trajectories which break ergodicity. The interactions between particle and wall atoms are mediated by a Lennard-Jones potential, so that an analytical treatment of the dynamics is not feasible, but making the system more physically realistic. In view of recent studies, which proved non-ergodicity for systems with scatterers interacting via smooth potentials, we find that the non-ergodic component of thephase space for energy levels typical of experiments, is surprisingly small, i.e. we conclude that the ergodic hypothesis is a reasonable approximation even for a single particle trapped in a nanopore. Due to the numerical scope of this work, our focus will be the onset of ergodic behavior which is evident on time scales accessible to simulations and experimental observations rather than ergodicity in the infinite time limit.

KW - Ergodic theory

KW - Statistical mechanics

KW - Dynamical systems

KW - Lyapunov exponents

M3 - Journal article

VL - 148

SP - 1156

EP - 1169

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 6

ER -

Bernardi S, Hansen JS, Frascolli F, Todd B, Dettmann C. Ergodicity of a single particle confined in a nanopore. Journal of Statistical Physics. 2012;148(6):1156-1169.