Density Matrix Theories in Quantum Physics

Robert Schade, Ebad Kamil, Peter E. Blöchl

In materials with strong electron correlation the proper treatment of local atomic physics described by orbital occupations is crucial. Reduced density-matrix functional theory is a natural extension of density functional theory for systems that are dominated by orbital physics. We review the current state of reduced density-matrix functional theory (RDMFT). For atomic structure relaxations or ab-initio molecular dynamics the combination of density functional theory (DFT) and dynamical mean-field theory (DMFT) possesses a number of disadvantages, like the cumbersome evaluation of forces. We therefore describe a method, DFT+RDMFT, that combines many-particle effects based on reduced density-matrix functional theory with a density functional-like framework. A recent development is the construction of density-matrix functionals directly from many-particle theory such as methods from quantum chemistry or many-particle Green’s functions. We present the underlying exact theorems and describe current progress towards quantitative functionals.

Ronald F. Fox

The theory of multiplicative stochastic processes has been shown to lead to a density matrix description of nonequilibrium quantum mechanical phenomena. In the present paper a detailed treatment of the approach to the uniform, microcanonical, and canonical equilibrium density matrices is presented. The canonical equilibrium density matrix is approached by the density matrix which represents a subsystem in contact with a constant temperature heat reservoir.

Roderick I. Sutherland

T. Nishiyama

Progress of Theoretical Physics Vol. 5 No. 6 (1950) pp. 909-919 An Algebraic Theory of the Density Matrix, I Kodi Husimi and Toshiyuki Nishiyama

O. J. E. Maroney