Results 1 
3 of
3
NonEquilibrium Statistical Mechanics of Anharmonic Chains Coupled to Two Heat Baths at Different Temperatures
, 1999
"... . We study the statistical mechanics of a finitedimensional nonlinear Hamiltonian system (a chain of anharmonic oscillators) coupled to two heat baths (described by wave equations). Assuming that the initial conditions of the heat baths are distributed according to the Gibbs measures at two differ ..."
Abstract

Cited by 53 (14 self)
 Add to MetaCart
. We study the statistical mechanics of a finitedimensional nonlinear Hamiltonian system (a chain of anharmonic oscillators) coupled to two heat baths (described by wave equations). Assuming that the initial conditions of the heat baths are distributed according to the Gibbs measures at two different temperatures we study the dynamics of the oscillators. Under suitable assumptions on the potential and on the coupling between the chain and the heat baths, we prove the existence of an invariant measure for any temperature difference, i.e., we prove the existence of steady states. Furthermore, if the temperature difference is sufficiently small, we prove that the invariant measure is unique and mixing. In particular, we develop new techniques for proving the existence of invariant measures for random processes on a noncompact phase space. These techniques are based on an extension of the commutator method of H ormander used in the study of hypoelliptic differential operators. 1. Intr...
Ergodic Properties of Classical Dissipative Systems I
 I. Acta Math
, 1998
"... We consider a class of models in which a Hamiltonian system A, with a finite number of degrees of freedom, is brought into contact with an infinite heat reservoir B. We develop the formalism required to describe these models near thermal equilibrium. Using a combination of abstract spectral techniqu ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
We consider a class of models in which a Hamiltonian system A, with a finite number of degrees of freedom, is brought into contact with an infinite heat reservoir B. We develop the formalism required to describe these models near thermal equilibrium. Using a combination of abstract spectral techniques and harmonic analysis we investigate the singular spectrum of the Liouvillean L of the coupled system A + B. We provide a natural set of conditions which ensure that the spectrum of L is purely absolutely continuous except for a simple eigenvalue at zero. It then follows from the spectral theory of dynamical systems (Koopmanism) that the system A + B is strongly mixing. From a probabilistic point of view, we study a new class of random processes on finite dimensional manifolds: nonMarkovian OrnsteinUhlenbeck processes. The paths of such a process are solutions of a random integrodifferential equation with Gaussian noise which is a natural generalization of the well known Langevin equ...
Statistical Mechanics of anharmonic lattices
 In Advances in Differential Equations and Mathematical Physics, Contemporary Mathematics 327
, 2003
"... Abstract. We discuss various aspects of a series of recent works on the nonequilibrium stationary states of anharmonic crystals coupled to heat reservoirs (see also [7]). We expose some of the main ideas and techniques and also present some open problems. 1. ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Abstract. We discuss various aspects of a series of recent works on the nonequilibrium stationary states of anharmonic crystals coupled to heat reservoirs (see also [7]). We expose some of the main ideas and techniques and also present some open problems. 1.