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We examine the thermal conductivity and bulk viscosity of a one-dimensional(1D) chain of particles with cubic-plus-quartic interparticle potentials and noon-site potentials. This system is equivalent to the FPU-alpha beta system in asubset of its parameter space. We identify three distinct frequency regimeswhich we call the hydrodynamic regime, the perturbative regime and thecollisionless regime. In the lowest frequency regime (the hydrodynamic regime)heat is transported ballistically by long wavelength sound modes. The modelthat we use to describe this behaviour predicts that as the frequency goes tozero the frequency dependent bulk viscosity and the frequency dependent thermalconductivity should diverge with the same power law dependence on frequency.Thus, we can define the bulk Prandtl number as the ratio of the bulk viscosityto the thermal conductivity (with suitable prefactors to render itdimensionless). This dimensionless ratio should approach a constant value asfrequency goes to zero. We use mode-coupling theory to predict the zerofrequency limit. Values of the bulk Prandtl number from simulations are inagreement with these predictions over a wide range of system parameters. In themiddle frequency regime, which we call the perturbative regime, heat istransported by sound modes which are damped by four-phonon processes. We callthe highest frequency regime the collisionless regime since at thesefrequencies the observing times are much shorter than the characteristicrelaxation times of phonons. The perturbative and collisionless regimes arediscussed in detail in the appendices.

Detailed Examination of Transport Coefficients in Cubic-Plus-Quartic Oscillator Chains