Temperature profile and boundary conditions in an anomalous heat transport model

Abstract

A framework for studying the effect of the coupling to the heat bath in models exhibiting anomalous heat conduction is described. The framework is applied to the harmonic chain with momentum exchange model where the non-trivial temperature profile is calculated. In this approach one first uses the hydrodynamic (HD) equations to calculate the equilibrium current-current correlation function in large but finite chains, explicitly taking into account the BCs resulting from the coupling to the heat reservoirs. Making use of a linear response relation, the anomalous conductivity exponent $\alpha$ and an integral equation for the temperature profile are obtained. The temperature profile is found to be singular at the boundaries with an exponent which varies continuously with the coupling to the heat reservoirs expressed by the BCs. In addition, the relation between the harmonic chain and a system of noninteracting L{é}vy walkers is made explicit, where different BCs of the chain correspond to different reflection coefficients of the L{é}vy particles.

12 pages, 2 figures

References in corpus (8)

• Heat Transport in low-dimensional systems
• A momentum conserving model with anomalous thermal conductivity in low dimension
• Local Temperature and Universal Heat Conduction in FPU chains
• Nonlinear Fluctuating Hydrodynamics in One Dimension: the Case of Two Conserved Fields
• Current fluctuations for anharmonic chains in thermal equilibrium
• Green-Kubo formula for heat conduction in open systems
• Exact scaling solution of the mode coupling equations for non-linear fluctuating hydrodynamics in one dimension
• Nonequilibrium Invariant Measure under Heat Flow