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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A combinatorial approach to the diagonal $ N$-representability problem


Author: Mark Laurance Yoseloff
Journal: Trans. Amer. Math. Soc. 190 (1974), 1-41
MSC: Primary 81.47
DOI: https://doi.org/10.1090/S0002-9947-1974-0337218-1
MathSciNet review: 0337218
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Abstract: The problem considered is that of the diagonal N-representability of a pth-order reduced density matrix, $ p \geq 2$, for a system of N identical fermions or bosons. A finite number M of allowable single particle states is assumed. The problem is divided into three cases, namely: Case I. $ M = N + p$ ; Case II. $ M < N + p$; Case III. $ M > N + p$. Using the theory of polyhedral convex cones, a complete set of necessary and sufficient conditions is first found for Case I. This solution is then employed to find such conditions for Case II. For Case III, two algorithms are developed to generate solutions for the problem, and examples of the usage of these algorithms are given.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0337218-1
Article copyright: © Copyright 1974 American Mathematical Society