Broken ergodicity and the geometry of rugged landscapes

D. L. Stein, Charles Newman

Research output: Contribution to journalArticle

Abstract

We study the nature and mechanisms of broken ergodicity (BE) in specific random walk models corresponding to diffusion on random potential surfaces, in both one dimension and high dimension. Using both rigorous results and nonrigorous methods, we confirm several aspects of the standard BE picture and show that others apply in one dimension, but need to be modified in higher dimensions. These latter aspects include the notions that a fixed temperature confining barriers increase logarithmically with time, that " components" are necessarily bounded regions of state space which depend on the observational time scale, and that the system continually revisits previously traversed regions of state space. We examine our results in the context of several experiments, and discuss some implications of our results for the dynamics of disordered and/or complex systems.

Original languageEnglish (US)
Pages (from-to)5228-5238
Number of pages11
JournalPhysical Review E
Volume51
Issue number6
DOIs
StatePublished - 1995

Fingerprint

Ergodicity
One Dimension
Higher Dimensions
State Space
geometry
Random Potential
Complex Systems
Random walk
Time Scales
complex systems
random walk
confining
Experiment
Model
temperature

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

Broken ergodicity and the geometry of rugged landscapes. / Stein, D. L.; Newman, Charles.

In: Physical Review E, Vol. 51, No. 6, 1995, p. 5228-5238.

Research output: Contribution to journalArticle

Stein, D. L. ; Newman, Charles. / Broken ergodicity and the geometry of rugged landscapes. In: Physical Review E. 1995 ; Vol. 51, No. 6. pp. 5228-5238.
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