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

Dye SK Sato
Phys. Rev. E 102, 012111 – Published 6 July 2020

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 β (FPU-β) lattices.

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  • Received 19 April 2020
  • Accepted 9 June 2020

DOI:https://doi.org/10.1103/PhysRevE.102.012111

©2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Dye SK Sato*

  • Disaster Prevention Research Institute, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan

  • *sato.daisuke.6r@kyoto-u.ac.jp

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Vol. 102, Iss. 1 — July 2020

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