Stochastic process leading to wave equations in dimensions higher than one

Details Stochastic process leading to wave equations in dimensions higher than one Stochastic process leading to wave equations in dimensions higher than one

2010-01-21

arxiv.org/abs/1001.3821v1

Phys. Rev. E 81, 021113 (2010)

Physics

Condensed Matter

Statistical Mechanics

5 pages

Scientific paper

Stochastic processes are proposed whose master equations coincide with classical wave, telegraph, and Klein-Gordon equations. Similar to predecessors based on the Goldstein-Kac telegraph process, the model describes the motion of particles with constant speed and transitions between discreet allowed velocity directions. A new ingredient is that transitions into a given velocity state depend on spatial derivatives of other states populations, rather than on populations themselves. This feature requires the sacrifice of the single-particle character of the model, but allows to imitate the Huygens' principle and to recover wave equations in arbitrary dimensions.

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