Eur. Phys. J. B 70, 217-227 (2009)
https://doi.org/10.1140/epjb/e2009-00224-2

Local electron distributions and diffusion in anharmonic lattices mediated by thermally excited solitons

¹ Instituto Pluridisciplinar, Universidad Complutense, Paseo Juan XXIII, 1, 28040 Madrid, Spain
² Dept. of Physics, Saratov State University, Astrakhanskaya 83, 410012 Saratov, Russia
³ Institut für Physik, Humboldt-Universität Berlin, Newtonstrasse 15, 12489 Berlin, Germany

Corresponding author: ^a ebeling@physik.hu-berlin.de

Received: 27 February 2009
Revised: 27 May 2009
Published online: 30 June 2009

Abstract

We study the excitation of solitons in lattices with Morse interactions in a wide temperature range and their influence on (free) electrons moving in the lattice. The lattice units (considered as “atoms" or “screened ion cores") are treated by classical Langevin equations. For visualizations the densities of the core (valence) electrons are in a first estimate represented by Gaussian densities, thus permitting to visualize lattice compressions. The evolution of the (free) electrons is modelled in the tight binding approximation first using Schrödinger equation and, subsequently, a stochastic description of the evolution as a Markov process. We investigate electron transfer assisted by solitons and solitonic influences on macroscopic transport in particular on diffusion. Then we consider the electron-lattice interaction and obtain numerical solutions of the simultaneously evolving Langevin and Pauli master equations. We show that the proposed mechanism of riding on thermal solitons is relatively fast (of the order of the sound velocity).