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On the properties of cumulant expansions
Author(s) -
Kladko K.,
Fulde P.
Publication year - 1998
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1998)66:5<377::aid-qua4>3.0.co;2-s
Subject(s) - cumulant , operator (biology) , infinitesimal , algebraic number , hilbert space , mathematics , expression (computer science) , connection (principal bundle) , wave function , mathematical analysis , physics , quantum mechanics , geometry , computer science , biochemistry , statistics , chemistry , repressor , transcription factor , gene , programming language
Cumulants represent a natural language for expressing macroscopic properties of a solid. We show that cumulants are subject to a nontrivial geometry. This geometry provides an intuitive understanding of a number of cumulant relations which have been obtained so far by using algebraic considerations. We give general expressions for their infinitesimal and finite transformations and represent a cumulant wave operator through an integration over a path in the Hilbert space. Cases are investigated where this integration can be done exactly. An expression of the ground‐state wave function in terms of the cumulant wave operator is derived. In the second part of the article, we derive the cumulant counterpart of Faddeev's equations and show its connection to the method of increments. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 377–389, 1998