Density matrix theory

K. Blum, Density matrix theory and applications. Plenum Press, New York, 1981,... 

Blum, K., 1981, Density Matrix Theory and Applications (Plenum, New York). 

Since the early days of quantum mechanics, the wave function theory has proven to be very successful in describing many different quantum processes and phenomena. However, in many problems of quantum chemistry and solid-state physics, where the dimensionality of the systems studied is relatively high, ab initio calculations of the structure of atoms, molecules, clusters, and crystals, and their interactions are very often prohibitive. Hence, alternative formulations based on the direct use of the probability density, gathered under what is generally known as the density matrix theory [1], were also developed since the very beginning of the new mechanics. The independent electron approximation or Thomas-Fermi model, and the Hartree and Hartree-Fock approaches are former statistical models developed in that direction [2]. These models can be considered direct predecessors of the more recent density functional theory (DFT) [3], whose principles were established by Hohenberg,... 

In the Hohenberg-Kohn formulation, the problem of the functional iV-representability has not been adequately treated, as it has been assumed that the 2-matrix IV-representability condition in density matrix theory only implies an N-representability condition on the one-particle density [21]. Because the latter can be trivially imposed [26, 27], the real problem has been effectively avoided. 

VARIATIONAL TWO-ELECTRON REDUCED-DENSITY-MATRIX THEORY... 

G. Gidofalvi and D. A. Mazziotti, Variational reduced-density-matrix theory strength of Hamiltonian-dependent positivity conditions. Chem. Phys. Lett. 398, 434 (2004). 

J. R. Hammond and D. A. Mazziotti, Variational two-electron reduced-density-matrix theory partial 3-positivity conditions for A-representability. Phys. Rev. A 71, 062503 (2005). 

R. M. Erdahl, Two algorithms for the lower bound method of reduced density matrix theory. Reports Math. Phys. 15, 147-162 (1979). 

R. McWeeny, Some recent advances in density matrix theory. Rev. Mod. Phys. 32, 335 (1960). 

M. D. Benayoun and A. Y. Lu, Invariance of the cumulant expansion under l-particle unitary transformations in reduced density matrix theory. Chem. Phys. Lett. 387, 485 (2004). 

J. M. Herbert, Reconstructive Approaches to One- and Two-Electron Density Matrix Theory, Ph.D. thesis, University of Wisconsin, Madison, WI, 2003. 

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