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QP-PQ, quantum probability and white noise analysis

Unitarity of solutions to quantum stochastic differential equations and conservativity of the associated semigroups

Franco Fagnola

Published Jul 1, 1992• 13 citations
Publisher
DOI
10.1142/9789814354783_0010

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If the Hamiltonian of the system is a bounded selfadjoint operator, we give a simple alternative characterization of the infinitesimal generator iC of the unitary group associated with a Quantum Stochastic Differential Equation (QSDE). By using the defect indices of the symmetric operator C, we give a sufficient condition that assures that iC is the restriction of a generator of a strongly continuous semigroup of isometries in the case when the Hamiltonian of the system is an unbounded symmetric operator.