What Is a Quantum Stochastic Differential Equation from the Point of View of Functional Analysis? |
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Authors: | A M Chebotarev |
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Institution: | (1) M. V. Lomonosov Moscow State University, Russia |
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Abstract: | We prove that a quantum stochastic differential equation is the interaction representation of the Cauchy problem for the Schrödinger equation with Hamiltonian given by a certain operator restricted by a boundary condition. If the deficiency index of the boundary-value problem is trivial, then the corresponding quantum stochastic differential equation has a unique unitary solution. Therefore, by the deficiency index of a quantum stochastic differential equation we mean the deficiency index of the related symmetric boundary-value problem.In this paper, conditions sufficient for the essential self-adjointness of the symmetric boundary-value problem are obtained. These conditions are closely related to nonexplosion conditions for the pair of master Markov equations that we canonically assign to the quantum stochastic differential equation. |
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Keywords: | Fock space quantum stochastic differential equation symmetric boundary-value problem deficiency index |
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