The quantum stochastic equation is unitarily equivalent to a symmetric boundary value problem for the Schrödinger equation
type: Item
instance of: scholarly article
title: The quantum stochastic equation is unitarily equivalent to a symmetric boundary value problem for the Schrödinger equation
zbMATH Open document ID: 0919.60093
DOI: 10.1007/BF02354995
published in: Mathematical Notes
publication date: 1999-08-31T00:00:00Z
review text: Solutions of Markov evolution equations in the theory of open quantum systems provide a stochastic representation of quantum dynamical semigroups (in particular those in von Neumann algebras). The author considers quantum stochastic differential equations whose solutions in the interaction representation are weak or strong resolvent limits of solutions of a family of Schrödinger equations in the Fock space. Functions that belong to the range of the resolvent of the limit unitary group are known to experience amplitude and phase jumps at points where the quadratic form of the generator has singularities. The corresponding Markov evolution equation (in the Lindblad form) is derived from the boundary value problem for the Schrödinger equation.
reviewed by: Piotr Garbaczewski
Mathematics Subject Classification ID: 60K40
Mathematics Subject Classification ID: 81S25
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 1238001
zbMATH Keywords: quantum noise
zbMATH Keywords: quantum dynamical semigroup
zbMATH Keywords: open quantum system
zbMATH Keywords: resolvent limit
author: Alexander M. Chebotarev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02354995
OpenAlex ID: W2124823331
description: scientific article; zbMATH DE number 1238001