Journal of Physical Studies 4(4), 371–379 (2000) DOI: https://doi.org/10.30970/jps.04.371 TELEGRAPH EQUATION IN RANDOM WALK PROBLEM V. V. Uchaikin, V. V. Saenko Ulyanovsk State University, Institute for Theoretical Physics, Ulyanovsk, 432700, Russia

The isotropic random walk of a particle with a constant speed is considered in the $d$-dimensional space. This process is described by the kinetic equation which has explicit solutions in terms of quadratures or special functions only in the cases $d=1$ and 2. For $d>2$, the two reduced forms of the equation are used: the telegraph equation and the diffusion equation. The latter is usually considered as a rougher approximation than the telegraph one. The numerical investigations performed in this article show that actually the situation is diametrically opposed: for $d \geq 2$ the simple diffusion result turns out to be closer to the exact one than the more complex solution of the telegraph equation. The results are applicable to surface transport and volume transport problem and can be useful for describing the chaotic dynamics of a system in terms of random walks in the phase space.

PACS number(s): 02.50.-r, 02.50.Ga, 02.60.-x, 05.60.+w

ps pdf