Self-energy part of the one-particle Green function

Giovanna Lani, Pina Romaniello, Lucia Reining

Th. Bornath, M. Schlanges, D. Kremp

Abstract The two‐particle problem within a nonequilibrium many‐particle system is investigated in the framework of real‐time Green's functions. A nonequilibrium Dyson equation is given for the two‐time two‐particle Green's function. The two‐particle self‐energy in this equation consists of two qualitatively different parts: one part is local in time, whereas the other part is a two‐time quantity having thus a dynamical character. The latter part of the self‐energy can be expressed in terms of multi‐particle Green's functions.

J. Schirmer, Giuliana Angonoa

The necessity to determine the static self-energy part Σ(∞) in many-body Green’s function studies of atomic and molecular ionization introduces difficulties affecting both the accuracy and the efficiency of the method. We show how this bottleneck can be overcome under an approximation obtained by truncating the Dyson expansion for the one-particle Green’s function G(ω). Here the essential computational step consists of an inversion or a Lanczos diagonalization of constant Hermitian secular matrices associated with the dynamical self-energy part M(ω). Both methods are very practical and efficient as is demonstrated in an exemplary application to the CO molecule. The same approximation and numerical techniques apply also to the problem of extracting ground state information from G(ω), i.e., correlation energy and expectation values of single-particle operators.

J. E. Young

W. E. Parry, Roy E. Turner

Some analytic properties of the single-particle Green functions and proper self-energy parts for a system of interacting bosons at nonzero temperatures are derived. In particular, it is shown how to obtain the analytical continuations of simple functions of the proper self-energy parts, which can be obtained from perturbation theory at an infinite set of points along the imaginary energy axis, to the whole of the complex energy plane. This is useful in determining the poles of the Green functions.