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Gibbs States of a Quantum Crystal: Uniqueness by Small Particle Mass by Sergio Albeverio; Yuri Kondratiev; Yuri Kozitsky; Michael Röckner is a Mathematics article available to read on EtoBox.

What is Gibbs States of a Quantum Crystal: Uniqueness by Small Particle Mass about?

A model of interacting quantum particles performing one-dimensional anharmonic oscillations around their unstable equilibrium positions, which form the lattice Z d , is considered. For this model, two statements describing its equilibrium properties are given. The first theorem states that there exists m \* > 0 such that for all values of the particle mass m < m \* , the set of tempered Euclidean Gibbs measures consists of exactly one element at all values of the temperature β -1 . This settles a problem that was open for a long time and is an essential improvement of a similar result proved before by the same authors [1] where the boundary m \* depended on β in such a way that m \* (β) → 0 for β → +∞. The second theorem states that the two-point correlation function has an exponential decay if m < m \* .

Who reads Gibbs States of a Quantum Crystal: Uniqueness by Small Particle Mass?

Author

Sergio Albeverio; Yuri Kondratiev; Yuri Kozitsky; Michael Röckner

Publisher

Elsevier Science; Elsevier ; Elsevier Masson; Elsevier BV; Cellule MathDoc/CEDRAM (ISSN 1631-073X)

Published

2002

Language

EN

Field

Mathematics (Physical Sciences)