Fluctuating hydrodynamics for a discrete Gross-Pitaevskii equation: mapping to Kardar-Parisi-Zhang universality class

We show that several aspects of the low-temperature hydrodynamics of a discrete Gross-Pitaevskii equation (GPE) can be understood by mapping it to a nonlinear version of fluctuating hydrodynamics. This is achieved by first writing the GPE in a hydrodynamic form of a continuity and an Euler equation. Respecting conservation laws, dissipation and noise due to the system's chaos are added, thus giving us a nonlinear stochastic field theory in general and the Kardar-Parisi-Zhang (KPZ) equation in our particular case. This mapping to KPZ is benchmarked against exact Hamiltonian numerics on discrete GPE by investigating the non-zero temperature dynamical structure factor and its scaling form and exponent. Given the ubiquity of the Gross-Pitaevskii equation (a.k.a. nonlinear Schrodinger equation), ranging from nonlinear optics to cold gases, we expect this remarkable mapping to the KPZ equation to be of paramount importance and far reaching consequences.Comment: 6 pages, 2 figure

On the convergence to statistical equilibrium for harmonic crystals

We consider the dynamics of a harmonic crystal in $d$ dimensions with $n$ components, $d,n$ arbitrary, $d,n\ge 1$, and study the distribution $\mu_t$ of the solution at time $t\in\R$. The initial measure $\mu_0$ has a translation-invariant correlation matrix, zero mean, and finite mean energy density. It also satisfies a Rosenblatt- resp. Ibragimov-Linnik type mixing condition. The main result is the convergence of $\mu_t$ to a Gaussian measure as $t\to\infty$. The proof is based on the long time asymptotics of the Green's function and on Bernstein's ``room-corridors'' method

Comment on ``Can Disorder Induce a Finite Thermal Conductivity in 1D Lattices?''

In a recent paper [Phys. Rev. Lett. 86, 63 (2001)], Li et al have reported that the nonequilibrium heat conducting steady state of a disordered harmonic chain is not unique. In this comment we point out that for a large class of stochastic heat baths the uniqueness of the steady state can be proved, and therefore the findings of Li et al could be either due to their use of deterministic heat baths or insufficient equilibration times in the simulations. We give a simple example where the uniquness of the steady state can be explicitly demonstrated.Comment: 1 page, 1 figure, accepted for publication in Phys. Rev. Let

A Combined System for Update Logic and Belief Revision

Revised Selected PapersInternational audienceIn this paper we propose a logical system combining the update logic of A. Baltag, L. Moss and S. Solecki (to which we will refer to by the generic term BMS, [BMS04]) with the belief revision theory as conceived by C. Alchourron, P. Gardenfors and D. Mackinson (that we will call the AGM theory, [GardRott95]) viewed from the point of view of W. Spohn ( [Spohn90], [Spohn88]). We also give a proof system and a comparison with the AGM postulates