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Stochastic process leading to wave equations in dimensions higher than one

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 نشر من قبل Alexander Plyukhin V
 تاريخ النشر 2010
  مجال البحث فيزياء
والبحث باللغة English
 تأليف A.V. Plyukhin




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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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