Bounded fluctuations and translation symmetry breaking: A solvable model

B. Jancovici; J. L. Lebowitz

doi:10.1023/A:1010349517967

Bounded fluctuations and translation symmetry breaking: A solvable model

B. Jancovici, J. L. Lebowitz

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The variance of the particle number (equivalently the total charge) in a domain of length ℒ of a one-component plasma (OCP) on a cylinder of circumference W at the reciprocal temperature β = 2, is shown to remain bounded as ℒ → χ. This exactly solvable system with average density p has a density profile which is periodic with period (pW)^-1 along the axis of the infinitely long cylinder. This illustrates the connection between bounded variance and periodicity in (quasi) one-dimensional systems.⁽¹⁾ When W → χ the system approaches the two-dimensional OCP and the variance in a domain A grows like its perimeter |∂Λ| In this limit, the system is translation invariant with rapid decay of correlations.

Original language	English (US)
Pages (from-to)	619-624
Number of pages	6
Journal	Journal of Statistical Physics
Volume	103
Issue number	3-4
DOIs	https://doi.org/10.1023/A:1010349517967
State	Published - May 1 2001

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Bounded fluctuations
Coulomb systems
Translation symmetry breaking

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AB - The variance of the particle number (equivalently the total charge) in a domain of length ℒ of a one-component plasma (OCP) on a cylinder of circumference W at the reciprocal temperature β = 2, is shown to remain bounded as ℒ → χ. This exactly solvable system with average density p has a density profile which is periodic with period (pW)-1 along the axis of the infinitely long cylinder. This illustrates the connection between bounded variance and periodicity in (quasi) one-dimensional systems.(1) When W → χ the system approaches the two-dimensional OCP and the variance in a domain A grows like its perimeter |∂Λ| In this limit, the system is translation invariant with rapid decay of correlations.

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