Anomalous Heat Diffusion

Peter Hänggi
University of Augsburg, Germany

Abstract:
In low dimensional systems the transport of heat in form of diffusive spread or heat flux be-tween reservoirs of differing ambient temperatures typically may exhibit anomalous features such as the violation of the Fourier Law with length-dependent heat conductivities or the dif-fusive spread of heat that occurs faster than normal.

Here we will discuss results and open issues (!) how the dynamics of energy spread occurring in one-dimensional nonlinear lattices relates to anomalous diffusion behavior and heat con-ductivities. Moreover we explain how the carriers of heat, typically referred to as phonons, may be given meaning in a regime with nonlinear interaction forces beyond the ballistic be-havior originating from solely harmonic (linear) interaction forces. The underlying physical mechanism of scattering then renders corresponding mean free paths of such effective pho-nons finite.

*Some pertinent own references are given below.

[1] A.V. Zarbudaev, S. Denisov and P. H?nggi, Perturbation spreading in many-particle systems: A random walk approach, Phys. Rev. Lett. 106: 180061(2011); ibid, Phys. Rev. Lett. 109, 069903 (2012).

[2] S. Liu, P. H?nggi, N. Li, J. Ren, and B. Li, Anomalous heat diffusion, Phys. Rev. Lett. 112: 040601 (2014)

[3] S. Liu, J. Liu, P. H?nggi, C. Wu, and B. Li, Triggering waves in Nonlinear Lattices: Quest for Anaharmonic Phonons and Corresponding Mean Free Paths, Phys. Reb. B (RC) 90, 174304 (2015)

[4] Y. Li, S. Liu, N. Li, P. H?nggi, and B. Li, 1D momemntum-conserving systems: the conundrum of anoma-lous versus normal heat transport, New J. Phys. 17, 043064 (2015)