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Updated: Apr 15, 2026

Characterization of Thermal Transport in One-dimensional Solid Materials
Published on: January 26, 2014
Universality classes for thermal transport in one-dimensional oscillator systems
1Math, Physics and Geology Department, Cape Breton University, Sydney, Nova Scotia, Canada, B1P 6L2.
Abstract:
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.
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