Detailed examination of transport coefficients in cubic-plus-quartic oscillator chains

We examine the thermal conductivity and bulk viscosity of a onedimensional (1D) chain of particles with cubicplusquartic interparticle potentials and no onsite potentials. This system is equivalent to the FPU-alpha beta system in a subset of its parameter space. We identify three distinct frequency regimes which we call the hydrodynamic regime, the perturbative regime and the collisionless regime. In the lowest frequency regime ( the hydrodynamic regime) heat is transported ballistically by long wavelength sound modes. The model that we use to describe this behaviour predicts that as omega --> 0 the frequency dependent bulk viscosity, (zeta) over cap(omega), and the frequency dependent thermal conductivity, (k) over tilde(omega), should diverge with the same power law dependence on.. Thus, we can define the bulk Prandtl number, Pr-zeta = k(B)(zeta) over cap (omega)/(m (k) over tilde(omega)), where m is the particle mass and k(B) is Boltzmann's constant. This dimensionless ratio should approach a constant value as omega --> 0. We use mode-coupling theory to predict the omega --> 0 limit of Pr-zeta Values of Pr-zeta obtained from simulations are in agreement with these predictions over a wide range of system parameters. In the middle frequency regime, which we call the perturbative regime, heat is transported by sound modes which are damped by fourphonon processes. This regime is characterized by an intermediatefrequency plateau in the value of (k) over tilde(omega). We find that the value of (k) over tilde(omega) in this plateau region is proportional to T-2 where T is the temperature; this is in agreement with the expected result of a fourphonon BoltzmannPeierls equation calculation. The BoltzmannPeierls approach fails, however, to give a nonvanishing bulk viscosity for all FPU-alpha beta chains. We call the highest frequency regime the collisionless regime since at these frequencies the observing times are much shorter than the characteristic relaxation times of phonons.