Gibbs states of a quantum crystal: uniqueness by small particle mass

✍ Scribed by Sergio Albeverio; Yuri Kondratiev; Yuri Kozitsky; Michael Röckner

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 74 KB
• Volume: 335
• Category: Article
• ISSN: 1631-073X
• DOI: 10.1016/s1631-073x(02)02545-1

✦ Synopsis

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 * .