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Thermal transport properties of the FPU $\beta$ model with a quadraticpinning term are investigated for various couplings and temperatures. Inparticular, the size dependence of the thermal conductivity, $\kappa\proptoL^\alpha$, is studied. $\alpha$ agrees with that of the FPU $\beta$ model (withno pinning) at high temperatures but decreases at low temperatures. Thiscrossover behavior occurs at a temperature depending on the strength of thequadratic pinning.

Some thermal transport properties of the FPU model with quadratic pinning