What is a quantum stochastic differential equation from the point of view of functional analysis?

被引：3

作者：

Chebotarev, AM ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Moscow 117234, Russia

来源：

MATHEMATICAL NOTES | 2002年 / 71卷 / 3-4期

基金：

俄罗斯基础研究基金会;

关键词：

Fock space; quantum stochastic differential equation; symmetric boundary-valve problem; deficiency index;

D O I：

10.1023/A:1014994726667

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that a quantum stochastic differential equation is the interaction representation of the Cauchy problem for the Schrodinger 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.

引用

页码：408 / 427

页数：20

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