On the stochastic limit for quantum theory

L. Accardi*, J. Gough, Y. G. Lu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The basic ideas of the stochastic limit for a quantum system with discrete energy spectrum, coupled to a Bose reservoir are illustrated through a detailed analysis of a general linear interaction: under this limit we have quantum noise processes substituting for the field. We prove that the usual Schrödinger evolution in interaction representation converges to a limiting evolution unitary on the system and noise space which, when reduced to system's degrees of freedom, provides the master and Langevin equations that are postulated on heuristic grounds by physicists. In addition, we give a concrete application of our results by deriving the evolution of an atomic system interacting with the electrodynamic field without recourse to either rotating wave or dipole approximations.

Original languageEnglish
Pages (from-to)155-187
Number of pages33
JournalReports on Mathematical Physics
Volume36
Issue number2-3
DOIs
Publication statusPublished - 1995

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