Gibbs ensembles for incompatible dependency networks

Limit shapes for Gibbs ensembles of partitions

We explicitly compute limit shapes for several grand canonical Gibbs ensembles of partitions of integers. These ensembles appear in models of aggregation and are also related to invariant measures of zero range and coagulation-fragmentation processes. We show, that all possible limit shapes for these ensembles fall into several distinct classes determined by the asymptotics of the internal ener...

Extended Gibbs ensembles with flow.

A recently proposed [Ph. Chomaz, F. Gulminelli, and O. Juillet, Ann. Phys. (Paris) 320, 135 (2005)] statistical treatment of finite unbound systems in the presence of collective motions is applied to a classical Lennard-Jones system, numerically simulated through molecular dynamics. In the ideal gas limit, the flow dynamics can be exactly recast into effective time-dependent Lagrange parameters...

Equivalence of Julesz and Gibbs Texture Ensembles

From Bosonic Grand-canonical Ensembles to Nonlinear Gibbs Measures

In a recent paper, in collaboration with Mathieu Lewin and Phan Thành Nam, we showed that nonlinear Gibbs measures based on Gross-Pitaevskii like functionals could be derived from many-body quantum mechanics, in a mean-field limit. This text summarizes these findings. It focuses on the simplest, but most physically relevant, case we could treat so far, namely that of the defocusing cubic NLS fu...

Complete Generalized Gibbs Ensembles in an Interacting Theory.

In integrable many-particle systems, it is widely believed that the stationary state reached at late times after a quantum quench can be described by a generalized Gibbs ensemble (GGE) constructed from their extensive number of conserved charges. A crucial issue is then to identify a complete set of these charges, enabling the GGE to provide exact steady-state predictions. Here we solve this lo...