The Hamiltonian Operator Associated with Some Quantum Stochastic Evolutions

Abstract:

We consider the Hamiltonian operator associated to the quantum stochastic differential equation introduced by Hudson and Parthasarathy to describe a quantum mechanical evolution in the presence of a “quantum noise”. We characterize such a Hamiltonian in the case of arbitrary multiplicity and bounded coefficients: we find an essentially self-adjoint restriction of the operator and, in particular, we provide an explicit construction of a dense set of vectors belonging to its domain.