Quantum stochastic analysis via white noise operators in weighted Fock space

Dong Myung Chung, Un Cig Ji, Nobuaki Obata

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)

Abstract

White noise theory allows to formulate quantum white noises explicitly as elemental quantum stochastic processes. A traditional quantum stochastic differential equation of Itô type is brought into a normal-ordered white noise differential equation driven by lower powers of quantum white noises. The class of normal-ordered white noise differential equations covers quantum stochastic differential equations with highly singular noises such as higher powers or higher order derivatives of quantum white noises, which are far beyond the traditional Itô theory. For a general normal-ordered white noise differential equation unique existence of a solution is proved in the sense of white noise distribution. Its regularity properties are investigated by means of weighted Fock spaces interpolating spaces of white noise distributions and associated characterization theorems for S-transform and for operator symbols.

Original languageEnglish
Pages (from-to)241-272
Number of pages32
JournalReviews in Mathematical Physics
Volume14
Issue number3
DOIs
Publication statusPublished - 2002 Aug 26

Keywords

  • Fock space
  • Normal-ordered white noise differential equation
  • Quantum stochastic differential equation
  • Quantum white noise
  • White noise theory
  • Wick product

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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