Universality classes for thermal transport in one-dimensional oscillator systems

Two universality classes for thermal transport in one-dimensional oscillator systems are proposed. In class A the asymptotic behavior of the frequency dependent thermal conductivity is κ(ω)~ω^-1/2, whereas the bulk viscosity is finite. In class B the asymptotic behavior of the thermal conductivity is κ~ω^-α, where α<0.4, and the frequency dependent bulk viscosity has the same asymptotic behavior as the thermal conductivity. It is further proposed that the criterion for membership in class A is that the ratio of specific heat capacities γ≡cP/cV=1. A one-dimensional cubic-plus-quartic coupled oscillator is examined at conditions for which γ=1 but P≠0. It is found that the system belongs to class A, in agreement with the proposed criterion. Additionally, it is proposed that examination of whether a system has a well-defined bulk Prandtl number is a more reliable way of determining whether a system is in class A or class B.