Universal scaling for recovery of Fourier's law in low-dimensional solids under momentum conservation

Abstract

Dynamic renormalization group (RG) of fluctuating viscoelastic equations is investigated to clarify the cause for numerically reported disappearance of anomalous heat conduction (recovery of Fourier's law) in low-dimensional momentum-conserving systems. RG flow is obtained explicitly for simplified two model cases: a one-dimensional continuous medium under low pressure and incompressible viscoelastic medium of arbitrary dimensions. Analyses of these clarify that the inviscid fixed point of contributing the anomalous heat conduction becomes unstable under the RG flow of nonzero elastic-wave speeds. The dynamic RG analysis further predicts a universal scaling of describing the crossover between the growth and saturation of observed heat conductivity, which is confirmed through the numerical experiments of Fermi-Pasta-Ulam $\beta$ (FPU-$\beta$) lattices.

16 pages, 2 figure

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• Phononic thermal properties of two-dimensional materials
• Non-integrability and the Fourier heat conduction law
• Universality of One-Dimensional Heat Conductivity
• Crossover from ballistic to normal heat transport in the ${\varphi }^4$ lattice: If nonconservation of momentum is the reason, what is the mechanism?
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Cited by in corpus (2)

• Equilibration of sinusoidal modulation of temperature in linear and nonlinear chains
• Effect of pressure on thermalization of one-dimensional nonlinear chains