Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2012-02-29
Phys. Rev. E 85, 021150 (2012)
Physics
Condensed Matter
Statistical Mechanics
12 pages, 9 figures
Scientific paper
10.1103/PhysRevE.85.021150
It has been alleged in several papers that the so called delayed continuous-time random walks (DCTRWs) provide a model for the one-dimensional telegraph equation at microscopic level. This conclusion, being widespread now, is strange, since the telegraph equation describes phenomena with finite propagation speed, while the velocity of the motion of particles in the DCTRWs is infinite. In this paper we investigate how accurate are the approximations to the DCTRWs provided by the telegraph equation. We show that the diffusion equation, being the correct limit of the DCTRWs, gives better approximations in $L_2$ norm to the DCTRWs than the telegraph equation. We conclude therefore that, first, the DCTRWs do not provide any correct microscopic interpretation of the one-dimensional telegraph equation, and second, the kinetic (exact) model of the telegraph equation is different from the model based on the DCTRWs.
Rukolaine Sergey A.
Samsonov Alexander M.
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