Bounded Fluctuations and Translation Symmetry Breaking: A Solvable Model |
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Authors: | B Jancovici J L Lebowitz |
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Institution: | (1) Laboratoire de Physique Théorique, Université de Paris-Sud, Bâtiment 210, 91405 Orsay, France;(2) Departments of Mathematics and Physics, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey, 08854-8019 |
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Abstract: | The variance of the particle number (equivalently the total charge) in a domain of length
of a one-component plasma (OCP) on a cylinder of circumference W at the reciprocal temperature =2, is shown to remain bounded as
. This exactly solvable system with average density has a density profile which is periodic with period (W)–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 the system approaches the two-dimensional OCP and the variance in a domain grows like its perimeter ||. In this limit, the system is translation invariant with rapid decay of correlations. |
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Keywords: | Coulomb systems bounded fluctuations translation symmetry breaking |
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