THERMAL TRANSPORT THROUGH A DIELECTRIC CHAIN WITH FERMI–PASTA–ULAM INTERACTIONS

Abstract

By means of the Ford–Kac–Mazur formalism, the heat current and local kinetic energy of a dielectric chain with Fermi–Pasta–Ulam–β nonlinear interactions are derived out in the stationary equilibrium and analyzed numerically. We find that the anharmonicity reduces the heat current for repulsive interactions and enhances the heat current for attractions. The magnitudes of heat current are relevant strong at low frequencies, while the local kinetic energy is bigger in the high-frequency regime. The local kinetic energy displays a periodic oscillation due to the interference of the thermal waves. In particular, the transmission matrix exhibits oscillations due to scattering of phonons for the imperfect contacts. In general, the thermal transport is qualitatively altered by the differences of temperature between reservoirs, nonlinear interactions and the size of chain as well as the contacts.