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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)
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. 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...
A GallavottiCohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
 J. STAT. PHYS
, 1999
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Thermal Conductivity for a Noisy Disordered Harmonic Chain
, 808
"... Abstract. We consider a ddimensional disordered harmonic chain (DHC) perturbed by an energy conservative noise. We obtain uniform in the volume upper and lower bounds for the thermal conductivity defined through the GreenKubo formula. These bounds indicate a positive finite conductivity. We prove ..."
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Cited by 5 (4 self)
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Abstract. We consider a ddimensional disordered harmonic chain (DHC) perturbed by an energy conservative noise. We obtain uniform in the volume upper and lower bounds for the thermal conductivity defined through the GreenKubo formula. These bounds indicate a positive finite conductivity. We prove also that the infinite volume homogenized GreenKubo formula converges. 1.
Heat transport in harmonic lattices
, 2009
"... We work out the nonequilibrium steady state properties of a harmonic lattice which is connected to heat reservoirs at different temperatures. The heat reservoirs are themselves modeled as harmonic systems. Our approach is to write quantum Langevin equations for the system and solve these to obtain ..."
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Cited by 2 (1 self)
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We work out the nonequilibrium steady state properties of a harmonic lattice which is connected to heat reservoirs at different temperatures. The heat reservoirs are themselves modeled as harmonic systems. Our approach is to write quantum Langevin equations for the system and solve these to obtain steady state properties such as currents and other second moments involving the position and momentum operators. The resulting expressions will be seen to be similar in form to results obtained for electronic transport using the nonequilibrium Green’s function formalism. As an application of the formalism we discuss heat conduction in a harmonic chain connected to selfconsistent reservoirs and reproduce some exact results on this model, obtained recently by Bonetto, Lebowitz and Lukkarinen.
unknown title
, 906
"... Thermal conductivity for a chain of anharmonic oscillators perturbed by a conservative noise ..."
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Thermal conductivity for a chain of anharmonic oscillators perturbed by a conservative noise