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Inequalities for fermion density matrices
Author(s) -
Garrod Claude,
Han J. Michael
Publication year - 1978
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.560130109
Subject(s) - density matrix , diagonal , matrix (chemical analysis) , trace (psycholinguistics) , mathematics , diagonal matrix , density of states , fermion , series (stratigraphy) , pure mathematics , mathematical analysis , mathematical physics , combinatorics , physics , quantum mechanics , chemistry , geometry , paleontology , linguistics , philosophy , chromatography , quantum , biology
A partial trace over the occupation numbers of all but k states in the density matrix of an ensemble with an arbitrary number of single‐particle states is defined as the (reduced) k ‐ state density matrix. This matrix is used to obtain a complete, practical solution to the problem of determining the representability of the diagonal elements of the one‐ and two‐particle (reduced) density matrices. This solution is expressed as a series of linear inequalities involving the density‐matrix elements; the inequalities are identical with those derived previously by Davidson and McCrae by a different method. In addition, our method is used to obtain nonlinear, matrix inequalities on the off ‐ diagonal elements of the density matrices.