Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Quantum Chemistry

Linear inequalities for density matrices: III

Ernest R. Davidson

Published Aug 13, 2002• 23 citations
Publisher

Abstract

Abstract Diagonal linear inequalities are derived for three‐ and four‐body reduced density matrices. These give a different insight into the previous derivations of linear inequalities for the two‐body reduced density matrix. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003
DOI
10.1002/qua.10340

Related papers

Reduced density matrices—Then and now*

Alan Coleman

Abstract The history and results of over forty years of research on the theory of reduced density matrices is discussed, and several key unsolved research problems announced. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001

International Journal of Quantum Chemistry•Jan 1, 2001•17 citations

Inequalities for fermion density matrices

Claude Garrod, James Michael Hannon

Abstract 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.

International Journal of Quantum Chemistry•Jan 1, 1978•4 citations

Linear Inequalities for Density Matrices

Ernest R. Davidson

A set of linear inequalities for the reduced two-body density matrix is presented. The general problem of finding all such inequalities is discussed. It is shown that all of the linear inequalities found so far for ensemble representability may be written as a single family of inequalities.

Journal of Mathematical Physics•Apr 1, 1969•80 citations

Some basic properties of the correlation matrices

Carmela Valdemoro, Luis M. Tel, Diego R. Alcoba +2 more

Abstract On the basis of the properties of correlation matrices, it is shown here that the set of all the first‐order transition reduced density matrices of a system provide complete information about that system. Also, the interrelation between the properties of the correlation matrix and the 2‐RDM N‐representability conditions is studied. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

International Journal of Quantum Chemistry•Jan 1, 2002•20 citations

Inequalities for phase‐space Rényi entropies

István Hornyák, Ágnes Nagy

Abstract Relations between different kinds of phase‐space Rényi and Shannon entropies are proved. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

International Journal of Quantum Chemistry•May 11, 2011•11 citations

INEQUALITIES RELATING THE ELEMENTS OF THE SECOND-ORDER REDUCED DENSITY MATRIX

Gergely Dezső, Imre Bálint, I.K. Gyémánt

The elements of the second-order reduced density matrix are pointed out to be written exactly as scalar products of specially defined vectors. Our considerations work in an arbitrarily large, but FInite orthonormal basis, and the underlying wave function is a full-CI type wave function. Using basic rules of vector operations, inequalities are formulated without the use of wave function, including only elements of density matrix.

Kluwer Academic Publishers eBooks•May 4, 2006•0 citations
Abstract 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.