arXiv subjects
Publications and source records attributed to Anouar Kouraich.
We show that Glauber dynamics for $ p$-spin glass mixes exponentially slowly at inverse temperatures larger than a constant times $ \ln (p)/p $ for large enough $ p $. This is done by analyzing the energy landscape using Gaussian decompositions and establishing a bottleneck bound.
We consider the free energy of a class of spin glass models with $ p$-spin interactions in a transverse magnetic field. As $ p \to \infty $, the infinite system-size free energy is proven to converge to that of the quantum random energy model. This is accomplished by combining existing analytical techniques addressing the non-commutative properties of such quantum glasses, with the description of the typical geometry of extreme negative deviations of the classical $ p $-spin glass. We also review properties of the corresponding classical free energy and conjectures addressing $ 1/p $-corrections in the quantum case.
Gibbs states play a central role in quantum statistical mechanics as the standard description of thermal equilibrium. Traditionally, their use is justified either by a heuristic, a posteriori reasoning, or by derivations based on notions of typicality or passivity. In this work, we show that Gibbs states are completely characterized by assuming dynamical stability of the system itself and of the system in weak contact with an arbitrary environment. This builds on and strengthens a result by Frigerio, Gorini, and Verri (1986), who derived Gibbs states from dynamical stability using an additional assumption that they referred to as the "zeroth law of thermodynamics", as it concerns a nested dynamical stability of a triple of systems. We prove that this zeroth law is redundant and that an environment consisting solely of harmonic oscillators is sufficient to single out Gibbs states as the only dynamically stable states.