Sergio Albeverio, Yuri Kondratiev, Yuri Kozitsky, Michael Roeckner
Small Mass Implies Uniqueness of Gibbs States of a Quantum Crystal
(472K, PDF)
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 $\beta \rightarrow +\infty$.