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Название: Bounded Fluctuations and Translation Symmetry Breaking in One-Dimensional Particle Systems
Авторы: Aizenman M., Goldstein S., Lebowitz J. L.
Аннотация:
We present general results for one-dimensional systems of point charges (signed
point measures) on the line with a translation invariant distribution + for which
the variance of the total charge in an interval is uniformly bounded (instead of
increasing with the interval length). When the charges are restricted to multiples
of a common unit, and their average charge density does not vanish, then the
boundedness of the variance implies translation-symmetry breakingin the
sense that there exists a function of the charge configuration that is nontrivially
periodic under translationsand hence that + is not 'mixing'.