Non-equilibrium dynamics of Dyson's model with an infinite number of particles

Makoto Katori, Hideki Tanemura

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

Dyson's model is a one-dimensional system of Brownian motions with longrange repulsive forces acting between any pair of particles with strength proportional to the inverse of distances with proportionality constant β/2. We give sufficient conditions for initial configurations so that Dyson's model with β = 2 and an infinite number of particles is well defined in the sense that any multitime correlation function is given by a determinant with a continuous kernel. The class of infinite-dimensional configurations satisfying our conditions is large enough to study non-equilibrium dynamics. For example, we obtain the relaxation process starting from a configuration, in which every point of ℤ is occupied by one particle, to the stationary state, which is the determinantal point process with the sine kernel.

Original languageEnglish
Pages (from-to)469-497
Number of pages29
JournalCommunications in Mathematical Physics
Volume293
Issue number2
DOIs
Publication statusPublished - 2009 Sep 18
Externally publishedYes

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Nonequilibrium Dynamics
Configuration
configurations
kernel
One-dimensional System
Point Process
Stationary States
determinants
Brownian motion
Well-defined
Correlation Function
Determinant
Directly proportional
Model
Sufficient Conditions

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Non-equilibrium dynamics of Dyson's model with an infinite number of particles. / Katori, Makoto; Tanemura, Hideki.

In: Communications in Mathematical Physics, Vol. 293, No. 2, 18.09.2009, p. 469-497.

Research output: Contribution to journalArticle

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