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Quadratic quantum white noises and Lévy Laplacian. (English) Zbl 1042.81557

Summary: As a generalization of a quantum stochastic differential equation, a normal-ordered white noise differential equation involving quadratic quantum white noises is 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.

MSC:

81S25 Quantum stochastic calculus
60H40 White noise theory
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