Some thermal transport properties of the FPU model with quadratic pinning

TL;DR

This paper investigates how quadratic pinning affects thermal conductivity in the FPU β model, revealing a temperature-dependent crossover in size dependence that aligns with the unpinned model at high temperatures.

Contribution

It provides new insights into the impact of quadratic pinning on thermal transport and the temperature-dependent crossover behavior in the FPU β model.

Findings

Thermal conductivity follows a power-law size dependence with exponent α.

At high temperatures, α matches the unpinned FPU β model.

At low temperatures, α decreases, indicating altered transport behavior.

Abstract

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.