02-504 Sergio Albeverio, Yuri Kondratiev, Yuri Kozitsky, Michael Roeckner

Small Mass Implies Uniqueness of Gibbs States of a Quantum Crystal (472K, PDF) Dec 6, 02

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Abstract. A model of interacting quantum particles performing one-dimensional anharmonic oscillations around their equilibrium positions which form a lattice $\mathbb{Z}^d$ is considered. For this model, it is proved that the set of tempered Euclidean Gibbs measures is a singleton provided the particle mass is less than a certain bound $m_*$, which is independent of the temperature $\beta^{-1}$. 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 \cite{AKKR1}, where the bound $m_*$ depended on $\beta$ in such a way that $m_* (\beta) \rightarrow 0$ as $\beta \rightarrow +\infty$.

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