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

Thermodynamic Chaos And The Structure Of Short-Range Spin Glasses

This paper presents an approach, recently introduced by the authors and based on the notion of \metastates", to the chaotic size dependence expected in systems with many competing pure states, and applies it to the Edwards-Anderson (EA) spin glass model. We begin by reviewing the standard picture of the EA model based on the Sherrington-Kirkpatrick (SK) model and why that standard SK picture is untenable. We then introduce metastates, which are the analogues of the invariant probability measures describing chaotic dynamical systems and discuss how they should appear in several models simpler than the EA spin glass. Finally, we consider possibilities for the nature of the EA metastate, including one which is a nonstandard SK picture, and speculate on their prospects. An appendix contains proofs used in our construction of metastates and in the earlier construction by Aizenman and Wehr. Research supported in part by NSF Grant DMS-9500868 y Research supported in part by DOE Grant DE-..

Sensitive Dependence of Gibbs Measures at Low Temperatures

The Gibbs measures of an interaction can behave chaotically as the temperature drops to zero. We observe that for some classical lattice systems there are interactions exhibiting a related phenomenon of sensitive dependence of Gibbs measures: An arbitrarily small perturbation of the interaction can produce significant changes in the low-temperature behavior of its Gibbs measures. For some one-dimensional XY models we exhibit sensitive dependence of Gibbs measures for a (nearest-neighbor) interaction given by a smooth function, and for perturbations that are small in the smooth category. We also exhibit sensitive dependence of Gibbs measures for an interaction on a classical lattice system with finite-state space. This interaction decreases exponentially as a function of the distance between sites; it is given by a Lipschitz continuous potential in the configuration space. The perturbations are small in the Lipschitz topology. As a by-product we solve some problems stated by Chazottes and Hochman.Comment: Minor corrections geared to improve the expositio