The Self-Energy Problem in Quantum Dielectrics

Hannes Bolterauer, P. Gillessen

Morrel H. Cohen

A generalized self-consistent field (SCF) theory of many-particle systems is developed by modifying the usual functional relationship between energy and wave function. A parameter $\ensuremath{\xi}$, $0\ensuremath{\le}\ensuremath{\xi}\ensuremath{\le}1$, is thus introduced into the energy so that for $\ensuremath{\xi}=0$, the particles interact only with a self-consistent field, for $\ensuremath{\xi}=1$ the particles interact dynamically among themselves with the correct field, and for intermediate values of $\ensuremath{\xi}$ both SCF and dynamical interactions occur. A systematic development of the theory is given for time-independent and time-dependent probelms, for finite temperatures, and for both uniform and nonuniform systems. The derivative with respect to $\ensuremath{\xi}$ of the total energy, of free energy, is expressed in terms of the dielectric function and an improved version of the dielectric formulation of the many-body problem thereby obtained. A brief discussion of the advantages of the method, possible applications, and further generalizations or extensions is included.

Stephen Mark Barnett

Claudio Verdozzi, Rex W. Godby, S. Holloway

We evaluate several approximations for the self-energy operator and dielectric function of systems of interacting electrons using a two-dimensional Hubbard cluster for which the self-energy, dielectric function, and one-particle Green's function may be calculated exactly. The results show the $\mathrm{GW}$ approximation (in the form in which it is commonly used in ab initio calculations for real materials) to be relatively successful in establishing the main features of the spectrum, even when the electron-electron interaction is not weak. It is also clear that improving the $G\mathrm{and}W$ used in this approximation without including vertex corrections in the self-energy does not lead to major improvements.

Andrey Nikolaevich Volobuev, Eugene S. Petrov

The laws of formation of the impulse of electromagnetic radiation in dielectric environment for conditions self-induced transparency are considered. The insufficiency of the description of such impulse with the help of the equations Maxwell-Bloch is shown. The way of connection of an average number filling and energy of the impulse taking into account energy saturation of environment are offered. The calculation of an electrical component of the impulse is submitted.

L. Allen, Stig Stenholm