Diffusion of a particle in the Gaussian random-energy landscape: Einstein relation and analytical properties of average velocity and diffusivity as functions of driving force

S. V. Novikov

Phys. Rev. E 98, 012128 – Published 23 July 2018

Abstract

We demonstrate that the Einstein relation for the diffusion of a particle in the random-energy landscape with the Gaussian density of states is an exclusive one-dimensional property and does not hold in higher dimensions. We also consider the analytical properties of the particle velocity and diffusivity for the limit of weak driving force and establish a connection between these properties and dimensionality and spatial correlation of the random-energy landscape.

Received 30 December 2017
Revised 19 March 2018

DOI:https://doi.org/10.1103/PhysRevE.98.012128

Physics Subject Headings (PhySH)

Brownian motion Diffusion Electrical conductivity Hopping transport Random walks Transport phenomena

Amorphous materials Disordered systems Organic compounds

Brownian dynamics Feynman diagrams Methods in transport

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

S. V. Novikov^*

A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Leninsky prosp. 31, 119071 Moscow, Russia and National Research University Higher School of Economics, Myasnitskaya Ulitsa 20, Moscow 101000, Russia

^*novikov@elchem.ac.ru

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Issue

Vol. 98, Iss. 1 — July 2018

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Physical Review E

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