Tatiana Pasurek

Euclidean Gibbs Measures of Interacting Quantum Anharmonic Oscillators

A rigorous description of the equilibrium thermodynamic properties of an infinite system of interacting ν-dimensional quantum anharmonic oscillators is given. The oscillators are indexed by the elements of a countable set

Gibbs states on loop lattices: existence and a priori estimates

{\mathbb L}\subset {\mathbb R}^d

Euclidean Gibbs Measures of Quantum Crystals: Existence, Uniqueness and a Priori Estimates

, possibly irregular; the anharmonic potentials vary from site to site and the interaction has infinite range. The description is based on the representation of the Gibbs states in terms of path measures—the so called Euclidean Gibbs measures. It is proven that: (a) the set of such measures

Euclidean Gibbs measures on loop lattices: Existence and a priori estimates

\mathcal{G}^{\rm t}

Gibbs States of Interacting Systems of Quantum Anharmonic Oscillators

is non-void and compact; (b) every