The Fourier heat conduction as a strong kinetic effect

Abstract

For an one-dimensional (1D) momentum conserving system, intensive studies have shown that generally its heat current autocorrelation function (HCAF) tends to decay in a power-law manner and results in the breakdown of the Fourier heat conduction law in the thermodynamic limit. This has been recognized to be a dominant hydrodynamic effect. Here we show that, instead, the kinetic effect can be dominant in some cases and leads to the Fourier law. Usually the HCAF undergoes a fast decaying kinetic stage followed by a long, slowly decaying hydrodynamic tail. In a finite range of the system size, we find that whether the system follows the Fourier law depends on whether the kinetic stage dominates. Our study is illustrated by the 1D diatomic gas model, with which the HCAF is derived analytically and verified numerically by molecular dynamics simulations.

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• The Taylor-von Neumann-Sedov blast-wave solution: comparisons with microscopic simulations of a one-dimensional gas
• Effect of pressure on thermalization of one-dimensional nonlinear chains
• Kinetic and hydrodynamic regimes in multi-particle-collision dynamics of a one-dimensional fluid with thermal walls
• Heat conduction in a three-dimensional momentum-conserving fluid
• A splash in a one-dimensional cold gas
• Chapman-Enskog theory and crossover between diffusion and superdiffusion for nearly integrable quantum gases
• Thermalization in asymmetric harmonic chains
• Phonon Gravity, Non-equilibrium QFT, and the Tolman Thermal Equivalence Principle
• From Near-Integrable to Far-from-Integrable: A Unified Picture of Thermalization and Heat Transport