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Phys Rev Lett. 2014 Jan 31;112(4):040601. Epub 2014 Jan 28.

Anomalous heat diffusion.

Author information

1
Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, 117546 Singapore and NUS Graduate School for Integrative Sciences and Engineering, 117456 Singapore.
2
Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, 117546 Singapore and Institute of Physics, University of Augsburg, Universitätsstrasse 1, D-86159 Augsburg, Germany and Nanosystems Initiative Munich, Schellingstr, 4, D-80799 München, Germany and Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, 200092 Shanghai, China.
3
Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, 200092 Shanghai, China.
4
Theoretical Division, Los Alamos National Laboratory, Los Alamos, 87545 New Mexico, USA.
5
Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, 117546 Singapore and NUS Graduate School for Integrative Sciences and Engineering, 117456 Singapore and Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, 200092 Shanghai, China.

Abstract

Consider anomalous energy spread in solid phases, i.e., <Δx(2)(t)>E≡∫(x-<x>E)(2)ρE(x,t)dx∝t(β), as induced by a small initial excess energy perturbation distribution ρE(x,t=0) away from equilibrium. The second derivative of this variance of the nonequilibrium excess energy distribution is shown to rigorously obey the intriguing relation d(2)<Δx(2)(t)>E/dt2=2CJJ(t)/(kBT(2)c), where CJJ(t) equals the thermal equilibrium total heat flux autocorrelation function and c is the specific volumetric heat capacity. Its integral assumes a time-local Helfand-like relation. Given that the averaged nonequilibrium heat flux is governed by an anomalous heat conductivity, the energy diffusion scaling determines a corresponding anomalous thermal conductivity scaling behavior.

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