On an operator identity central to projection operator methodology

Wilson Lamb, Ian Murdoch, John Stewart

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Derivations of master equations using projection operator methodology are based upon an identity whose validity has been established in only limited contexts. Its proof requires precise definitions of eLt and , where L is the Liouville operator and P the projection operator associated with the limited system information of interest. Here, for interacting particles confined to a box, the existence and uniqueness of system dynamics is demonstrated. A distributional extension of L defined in an L1 space is derived for which is the corresponding updating operator. Attempts to define within current semigroup theory are outlined, and a possible future approach indicated.
LanguageEnglish
Pages121-139
Number of pages18
JournalPhysica A: Statistical Mechanics and its Applications
Volume298
Issue number1
DOIs
Publication statusPublished - 3 Aug 2001

Fingerprint

Projection Operator
projection
methodology
operators
Semigroup Theory
Methodology
Master Equation
Operator
System Dynamics
Updating
Existence and Uniqueness
information systems
uniqueness
boxes
derivation
Context

Keywords

  • liouville operator
  • projection operator
  • equations
  • semigroup theory

Cite this

Lamb, Wilson ; Murdoch, Ian ; Stewart, John. / On an operator identity central to projection operator methodology. In: Physica A: Statistical Mechanics and its Applications. 2001 ; Vol. 298, No. 1. pp. 121-139.
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On an operator identity central to projection operator methodology. / Lamb, Wilson; Murdoch, Ian; Stewart, John.

In: Physica A: Statistical Mechanics and its Applications, Vol. 298, No. 1, 03.08.2001, p. 121-139.

Research output: Contribution to journalArticle

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