Diffusion in a Half-Space: From Lord Kelvin to Path Integrals

Details Diffusion in a Half-Space: From Lord Kelvin to Path Integrals Diffusion in a Half-Space: From Lord Kelvin to Path Integrals

2004-06-24

arxiv.org/abs/cond-mat/0406613v1

Am. J. Phys. 73, 308-314 (2005)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1119/1.1842734

Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling relations and stable distribution functions. In this paper, I present a treatment of a random walk confined to a half--space using a number of different approaches: diffusion equations, lattice walks and path integrals. Potential generalizations are discussed critically.

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