Quantum stochastic analysis via white noise operators in weighted Fock space

Dong Myung Chung, Un Cig Ji, Nobuaki Obata

研究成果: Article査読

28 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)241-272
ページ数32
ジャーナルReviews in Mathematical Physics
14
3
DOI
出版ステータスPublished - 2002

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

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