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Dynamical contribution to the heat conductivity in stochastic energy exchanges of locally confined gases

par Gaspard, Pierre ;Gilbert, Thomas
Référence Journal of Statistical Mechanics: Theory and Experiment, 2017, 4, 043210
Publication Publié, 2017-04

Article révisé par les pairs

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Résumé :

We present a systematic computation of the heat conductivity of the Markov jump process modeling the energy exchanges in an array of locally confined hard spheres at the conduction threshold. Based on a variational formula (Sasada 2016 (arXiv:1611.08866)), explicit upper bounds on the conductivity are derived, which exhibit a rapid power-law convergence towards an asymptotic value. We thereby conclude that the ratio of the heat conductivity to the energy exchange frequency deviates from its static contribution by a small negative correction, its dynamic contribution, evaluated to be -0.000 373 in dimensionless units. This prediction is corroborated by kinetic Monte Carlo simulations which were substantially improved compared to earlier results.