Heat flow in anharmonic crystals with internal and external stochastic baths: a convergent polymer expansion for a model with discrete time and long range interparticle interaction

DOI10.1088/1751-8113/48/37/375203zbMATH Open1329.82047arXiv1411.3820OpenAlexW3103268867MaRDI QIDQ3448426

Mateus S. Mendonça, Humberto C. F. Lemos, Emmanuel A. Pereira

Publication date: 23 October 2015

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Abstract: We investigate a chain of oscillators with anharmonic on-site potentials, with long range interparticle interactions, and coupled both to external and internal stochastic thermal reservoirs of Ornstein-Uhlenbeck type. We develop an integral representation, a la Feynman-Kac, for the correlations and the heat current. We assume the approximation of discrete times in the integral formalism (together with a simplification in a subdominant part of the harmonic interaction) in order to develop a suitable polymer expansion for the model. In the regime of strong anharmonicity, strong harmonic pinning, and for the interparticle interaction with integrable polynomial decay, we prove the convergence of the polymer expansion uniformly in volume (number of sites and time). We also show that the two-point correlation decays in space such as the interparticle interaction. The existence of a convergent polymer expansion is of practical interest: it establishes a rigorous support for a perturbative analysis of the heat flow problem and for the computation of the thermal conductivity in related anharmonic crystals, including those with inhomogeneous potentials and long range interparticle interactions.

Full work available at URL: https://arxiv.org/abs/1411.3820

zbMATH Keywords

heat flowanharmonic crystalspolymer expansion

Mathematics Subject Classification ID

Statistical mechanics of polymers (82D60) Statistical mechanics of crystals (82D25) Stochastic methods applied to problems in equilibrium statistical mechanics (82B31) Statistical thermodynamics (82B30)

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