On an operator identity central to projection operator methodology

Wilson Lamb, Ian Murdoch and John Stewart

Physica A: Statistical Mechanics and its Applications, 2001, vol. 298, issue 1, 121-139

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 e(I−P)L(I−P)t, 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 L of L defined in an L1 space is derived for which eLt is the corresponding updating operator. Attempts to define e(I−P)L(I−P)t within current semigroup theory are outlined, and a possible future approach indicated.

Keywords: Liouville operator; Projection operator identity; Semigroups of operators (search for similar items in EconPapers)
Date: 2001
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S037843710100214X
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:298:y:2001:i:1:p:121-139

DOI: 10.1016/S0378-4371(01)00214-X

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().