Density-functional formula for strongly correlated systems

O. Gunnarsson, O. K. Andersen, A. Svane

John P. Perdew

Huai‐Yu Wang, Rushan Han, Chen Nanxian

Density functional method is applied for strongly correlated systems. Based on the assumption that the systems are composed of electrons in singly-occupied orbitals and those in doubly-occupied orbitals, a set of self-consistent equations are obtained by standard variation procedure. The equations consist of two parts. One part is to solve the wave functions of the electrons in singly-occupied orbitals and the other is to solve the wave functions of the electrons in doubly-occupied orbitals. The physical meanings of the terms aspearing in the equations are discussed.

David Bernhard Blaschke, GERD RÖPKE, Gordon Baym

ABSTRACT We derive a generalized Beth–Uhlenbeck formula for the entropy of a dense fermion system with strong two‐particle correlations, including scattering states and bound states. We work within the Φ‐derivable approach to the thermodynamic potential. The formula takes the form of an energy‐momentum integral over a statistical distribution function times a unique spectral density. In the near mass‐shell limit, the spectral density reduces, contrary to naïve expectations, not to a Lorentzian but rather to a “squared Lorentzian” shape. The relation of the Beth–Uhlenbeck formula to the Φ‐derivable approach is exact at the two‐loop level for Φ. The formalism we develop, which extends the Beth–Uhlenbeck approach beyond the low‐density limit, includes Mott dissociation of bound states, in accordance with Levinson's theorem, and the self‐consistent back reaction of correlations in the fermion propagation. We discuss applications to further systems, such as quark matter and nuclear matter.

Robert O. Jones

Fang Jin-Qing

In this work,we present a nonequilibrium ensemble formalism based on the subdynamic kine-tic equation.The constructing procedure is to take a similarity transformation to Gibbsian ensemble formalism.This allows one to obtain subdynamic ensemble formalism for projected density operator.This formalism can be considered as a generalization of the equilibrium quantum canonical ensemble formula in the sense as 1) if the similarity operator is unitary,then the new formula is just an effective representation of the old canonical ensemble formula,2) if the similarity operator is non-unitary,then the new formula is an extension of the old formula,which represents a kind of non-equilibrium quantum canonical ensembles formula and reflects irreversibility of the system,and 3) if the similarity operator can be deduced by some approximations,such as Markovian/non-Markovian approximations,then the new formula can expose some irreversibility characteristics of the system which can not be gained from the equilibrium quantum ensemble formulas.As an application,we study a quantum strongly correlated network described by an Anderson model.A Green function based on this formalism is also introduced.We find the complex entropy of the system to be related to appearance of the local magnetic vectors in the nodes of the network,where the image part of the entropy represents an evolution rate of the entropy.