Thermal transport in the Fermi-Pasta-Ulam model with long-range interactions

Abstract

We study the thermal transport properties of the one dimensional Fermi-Pasta-Ulam model ($β$-type) with long-range interactions. The strength of the long-range interaction decreases with the (shortest) distance between the lattice sites as ${distance}^{-δ}$, where $δ\ge 0$.Two Langevin heat baths at unequal temperatures are connected to the ends of the one dimensional lattice via short-range harmonic interactions that drive the system away from thermal equilibrium. In the nonequilibrium steady state the heat current, thermal conductivity and temperature profiles are computed by solving the equations of motion numerically. It is found that the conductivity