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Springer eBooks

Multichannel Quantum-Classical Diffusion Equations

Michael V. Basilevsky, A. I. Voronin

Published Jan 1, 2003• 0 citations
Publisher
DOI
10.1007/978-94-010-0113-7_33

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We use a discrete approximation of quantum mechanics called the quantum random walk to study diffusion in one-dimensional crystalline nanostructures. There, intense fluctuations in the density are a consequence of quantum interference. As the size of the crystal increase, relative quantum fluctuations decrease and, if a coarse-grained averaging is taken, interference may be neglected. When this happens, we describe a far-from-equilibrium, classical, dynamic mesoscopic diffusion regime. In this regime, diffusion equations are given by a persistent-random-walk process. Density becomes a second-order Markov process, and in the continuum limit, the current satisfies the non-Fickian Maxwell-Cattaneo relationship. The generalized diffusion equation in the telegraphist's equation.