Uniqueness of Gibbs Measure for Models With Uncountable Set of Spin Values on a Cayley Tree

We consider models with nearest-neighbor interactions and with the set $[0,1]$ of spin values, on a Cayley tree of order $k\geq 1$. It is known that the "splitting Gibbs measures" of the model can be described by solutions of a nonlinear integral equation. For arbitrary $k\geq 2$ we find a sufficient condition under which the integral equation has unique solution, hence under the condition the corresponding model has unique splitting Gibbs measure.Comment: 13 page

Phonon distributions of a single bath mode coupled to a quantum dot

The properties of an unconventional, single mode phonon bath coupled to a quantum dot, are investigated within the rotating wave approximation. The electron current through the dot induces an out of equilibrium bath, with a phonon distribution qualitatively different from the thermal one. In selected transport regimes, such a distribution is characterized by a peculiar selective population of few phonon modes and can exhibit a sub-Poissonian behavior. It is shown that such a sub-Poissonian behavior is favored by a double occupancy of the dot. The crossover from a unequilibrated to a conventional thermal bath is explored, and the limitations of the rotating wave approximation are discussed.Comment: 21 Pages, 7 figures, to appear in New Journal of Physics - Focus on Quantum Dissipation in Unconventional Environment

An Ergodic Description of Ground States

Given a translation-invariant Hamiltonian H , a ground state on the lattice Z d is a configuration whose energy, calculated with respect to H , cannot be lowered by altering its states on a finite number of sites. The set formed by these configurations is translation-invariant. Given an observable defined on the space of configurations, a minimizing measure is a translation-invariant probability which minimizes the average of. If 0 is the mean contribution of all interactions to the site 0, we show that any configuration of the support of a minimizing measure is necessarily a ground state