Some thermal transport properties of the FPU model with quadratic pinning

Thermal transport properties of the FPU $\beta$ model with a quadratic pinning term are investigated for various couplings and temperatures. In particular, the size dependence of the thermal conductivity, $\kappa\propto L^\alpha$, is studied. $\alpha$ agrees with that of the FPU $\beta$ model (with no pinning) at high temperatures but decreases at low temperatures. This crossover behavior occurs at a temperature depending on the strength of the quadratic pinning.