Quadratic quantum white noises and Lévy Laplacian

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As a generalization of a quantum stochastic differential equation, a normal-ordered white noise differential equation involving quadratic quantum white noises are formulated on the basis of white noise theory. The solution is found in a Fock space singular to the original one. The classical process determined by the solution is unexpectedly related to a heat type equation associated with the Lévy Laplacian through Laplace transform.

Original languageEnglish
Pages (from-to)2437-2448
Number of pages12
JournalNonlinear Analysis, Theory, Methods and Applications
Issue number4
Publication statusPublished - 2001 Aug


  • Lévy Laplacian
  • Normal-ordered white noise equation
  • Quadratic quantum white noise
  • White noise theory


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