Anomalous heat equation in a system connected to thermal reservoirs

Priyanka; Aritra Kundu; Abhishek Dhar; Anupam Kundu

doi:10.1103/physreve.98.042105

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arXiv · 1803.06857

Anomalous heat equation in a system connected to thermal reservoirs

Priyanka·Aritra Kundu·Abhishek Dhar·Anupam Kundu

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Abstract

We study anomalous transport in a one-dimensional system with two conserved quantities in presence of thermal baths. In this system we derive exact expressions of the temperature profile and the two point correlations in steady state as well as in the non-stationary state where the later describes the relaxation to the steady state. In contrast to the Fourier heat equation in the diffusive case, here we show that the evolution of the temperature profile is governed by a non-local anomalous heat equation. We provide numerical verifications of our results.

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Priyanka, Aritra Kundu, Abhishek Dhar, Anupam Kundu. 2018-03-19. Anomalous heat equation in a system connected to thermal reservoirs. https://doi.org/10.1103/physreve.98.042105

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