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Extension of the cumulant definition for low particle number systems
Author(s) -
Kong Liguo
Publication year - 2011
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/qua.22832
Subject(s) - cumulant , rank (graph theory) , mathematics , constraint (computer aided design) , extension (predicate logic) , quantum , statistical physics , edgeworth series , quantum mechanics , physics , combinatorics , statistics , computer science , geometry , programming language
Cumulants are usually interpreted as the connected components of density matrices, but this interpretation fails and practical problems arise when the rank n of cumulants is larger than the number of particles ( N ) in the system. In that case, cumulants defined in the traditional way become disconnected. To solve this problem, the definition of cumulants is extended by introducing a simple modulation factor. The modified cumulants reduce to the conventional definition, but they vanish when N < n . Using the modified definition also eliminates the error in the approximation of density matrices by low‐rank cumulants, when N < n . The problem assumes a slightly different form when we work with active space–based theories, and it can be solved by a similar approach. Another problem with cumulants, due to spin coupling [Herbert, Int J Quantum Chem 2007, 107, 703], can be solved via the introduction of a similar modulation factor. A related yet more serious issue, termed as the local particle number constraint problem, is also discussed. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011