ИСТИНА

Strong resolvent convergence of Schrodinger evolution to quantum stochastic is proved for a class of Hamiltonians including a model of quantum detector of gravitational waves. It turns out that the limit of the sequence of self-adjoint Hamiltonians is a symmetric boundary value problem in Fock space. By using integration by parts in Fock space, we prove that this boundary value problem is unitarily equivalent to a quantum stochastic differential equation. By the deciency index of a quantum stochastic differential equation, we mean the deciency index of the related symmetric boundary value problem. If the deciency index of the boundary value problem is trivial, then the corresponding quantum stochastic differential equation has a unique unitary solution. Conditions sufcient for the essential self-adjointness of the symmetric boundary value problem were obtained in [1]. These conditions are closely related to nonexplosion conditions [2] for the pair of master Markov equations, which we canonically assign to the quantum stochastic differential equation. [1] A. M. Chebotarev, What is a quantum stochastic differential equation from the point of view of functional analysis?. Mathematical Notes, v.71, N3, Kluwer Academic - Plenum Publishers, New-York, 2002. [2] A. M. Chebotarev, Conditions Sufcient for the Conservativity of a Minimal Quantum Dynamical Semigroup. Mathematical Notes, v.71, N5, Kluwer Academic - Plenum Publishers, New-York, 2002.