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Review ARTICLE Provisionally accepted The full-text will be published soon. Notify me

Front. Phys. | doi: 10.3389/fphy.2019.00159

Anomalous heat transport in one dimensional systems: a description using non-local fractional-type diffusion equation

 Abhishek Dhar1,  Anupam Kundu1* and Aritra Kundu2
  • 1International Centre for Theoretical Sciences, ICTS, India
  • 2Raman Research Institute, India

It has been observed in many numerical simulations, experiments and from various theoretical treatments that heat transport in one-dimensional systems of interacting particles cannot be described by the phenomenological Fourier's law.
The picture that has emerged from studies over the last few years is that Fourier's law gets replaced by a spatially non-local linear equation wherein the current at a point gets contributions from temperature gradients in other parts of the system. Correspondingly the usual heat diffusion equation gets replaced by a non-local fractional-type diffusion equation.
In this review, we describe the various theoretical approaches which lead to this framework and also discuss recent progress on this problem.

Keywords: Fractional diffusion equation, Levy walks, Anomalous heat transport, Fluctuating hydrodynamics, Heat conduction

Received: 18 Jun 2019; Accepted: 30 Sep 2019.

Copyright: © 2019 Dhar, Kundu and Kundu. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Dr. Anupam Kundu, International Centre for Theoretical Sciences, ICTS, Bangalore, 560089, Karnataka, India, anupam.kundu@icts.res.in