One-body Green Function Research Articles

One-body Green's function for atoms and molecules: theory and application

The one-body Green's function is investigated by expanding the self-energy part up to third order. On this level some properties of the diagrams of the self-energy part are discussed. To estimate the contribution of higher orders of the self-energy part an effective time dependent interaction is introduced. It is found that the main contributions due to this interaction can be determined by considering the analytic properties of second and third order terms only. The numerical effort required can thus be strongly reduced. The theory is applied to calculate the vertical ionization potentials of B2H6. The calculation of the pole strengths shows that one may expect satellite lines in the photoelectron spectrum of B2H6 with about 10% of the intensity of the principal valence lines due to excitations accompanying ionization.

Damping of nuclear dipole states: Carl B. Dover and R. H. Lemmer. Institut de Physique Nucléaire, Division de Physique Théorique, 91—Orsay—France and F.J.W. Hahne. National Physical Research Laboratory, C.S.I.R., Pretoria, South Africa

Proton-hole spectral functions are calculated by solving the Dyson equation for the one-body Green function using a realistic G-matrix interaction. The consequences of replacing non-interacting intermediate states in the second-order self-energy by interacting ones is studied. These interactions are treated in Tamm-Dancoff approximation (TDA) as well as in random-phase approximation (RPA) for particle-hole or particle-particle (hole-hole) correlations. The influence of these correlations is illustrated for the spectral-strength distributions in 48Ca and 90Zr. The influence of a more realistic treatment of the states to which the particles couple is particularly strong at low energy, where such coherence phenomena are most important and where they yield additional fragmentation of single-particle strength. In accord with this observation, an increased depletion of mostly filled shells just below the Fermi energy and an increased occupation of mostly empty shells just above the Fermi energy is obtained. Instabilities found in the RPA treatment, point to the need of a self-consistent approach. Comparison with recent (e,e′p) data yields an estimate of about 10–15% for the amount of strength that is depleted by short-range correlations.

Green-function theory of transport coefficients I. General kinetic equations

The hierarchy equations governing the evolution of one-body Green functions can rigorously be transformed into closed equations in the bulk limit. The latter equations are non-markoffian and explicitly depend on the particle correlation to be given at an initial time. For the purpose of calculating a transport coefficient, the closed equations are shown to be greatly simplified into general kinetic equations without the loss of rigour. The kinetic equations are markoffian, and no longer depend on the initial condition. They provide a firm basis from which one can rigorously calculate linear and nonlinear transport coefficients of an imperfect quantum gas.

Resolution of the Hierarchy of Green's Functions for Fermions

The rigorous evolution equations for the one-body Green's functions (${g}^{g},{g}^{l}$) describing a system of interacting fermions are not closed (an analog of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for many-body distribution functions). The analysis of these equations is made in terms of proper connected diagrams. It is established that in the bulk limit, $N$ (particle number) $\ensuremath{\rightarrow}\ensuremath{\infty}$, $\ensuremath{\Omega}$ (volume) $\ensuremath{\rightarrow}\ensuremath{\infty}$ while $\frac{N}{\ensuremath{\Omega}}$ remains finite, these equations can rigorously be transformed into closed equations with respect to (${g}^{g},{g}^{l}$).

Resolution of the Hierarchy of Many-Body Green's Functions

The rigorous evolution equations for the one-body Green's functions ( g > , g < ) describing an imperfect gas in a finite volume are not closed (an analogue of B–B–G–K–Y hierarchy for the many-body distribution functions). The analysis of these equations are made in terms of proper connected diagrams. It is shown that in the bulk limit: N (particle number)→∞, \(\varOmega\)(volume)→∞ such that N /Ω=constant, these equations can be reduced to the closed equations, which are however, non-linear and non-Markoffian, in contrast to the original hierarchy equations.

Quasi-particle formulation of quantum statistics

Results are presented which express the thermodynamical functions of a normal inhomogeneous system as stationary functionals of a matrix Φ mn . The eigenvalues of Φ are “quasi-particle” occupation numbers. The relationship with Landau theory of Fermi liquids is discussed. The rules necessary to construct the relevant functionals of Φ, including the one-body Green's function, in powers of the two-body interaction, are explicited.

Uniqueness Property of the Twofold Vacuum Expectation Value

It is shown under general assumptions that if the onebody Green's function equals its free-field value the theory is that of a free field. (auth)