Single Particle Green's Function in the Electron–Plasmon Approximation

A discussion of how to carry out a direct perturbation expansion for the one-electron Green's function is given using an electron–plasmon model for the conduction electron correlations. A crucial feature of the method is the consistent extraction of energy shifts. Numerical results for the spectral function and the density of states are given in lowest order and the generalization to higher order is discussed. The present work differs from previous ones in that the method used cannot give rise to "plasmaron"-like excitations. Other singular features also come in differently.

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Real-space Green's-function approach within RHEED

Acta Crystallographica Section A Foundations of Crystallography ◽

10.1107/s0108767398007533 ◽

1999 ◽

Vol 55 (2) ◽

pp. 133-142

Author(s):

P. M. Derlet ◽

A. E. Smith

Keyword(s):

Green’S Function ◽

Density Of States ◽

Green's Function ◽

Local Density ◽

Perturbation Expansion ◽

Surface Region ◽

High Energy ◽

Real Space ◽

Resonance Phenomenon ◽

Total Density

Green's-function techniques are used to obtain a real-space series solution for the elastic reflection high-energy electron diffraction (RHEED) from a crystalline surface. A renormalized perturbation expansion due to potential self-scattering is developed for the local real-space Green's function. With the Pt (111) surface as an example, numerical results are obtained for reflection coefficients and intensities. In particular, calculations are performed to obtain the local density of states at and near the surface region. Total density-of-states calculations are also performed. These provide a basis for a discussion of the form of resonant electronic Green's functions that can be used to describe the surface resonance phenomenon within RHEED.

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Thermodynamic Green’s Functions and Spectral Structure

10.1093/oso/9780198791942.003.0007 ◽

2018 ◽

Author(s):

Norman J. Morgenstern Horing

Keyword(s):

Green’S Function ◽

Green's Function ◽

Green's Functions ◽

Green’S Functions ◽

Spectral Weight ◽

Statistical Thermodynamic ◽

Spectral Structure ◽

Imaginary Time ◽

Translational Invariance ◽

The One

Multiparticle thermodynamic Green’s functions, defined in terms of grand canonical ensemble averages of time-ordered products of creation and annihilation operators, are interpreted as tracing the amplitude for time-developing correlated interacting particle motions taking place in the background of a thermal ensemble. Under equilibrium conditions, time-translational invariance permits the one-particle thermal Green’s function to be represented in terms of a single frequency, leading to a Lehmann spectral representation whose frequency poles describe the energy spectrum. This Green’s function has finite values for both t>t′ and t<t′ (unlike retarded Green’s functions), and the two parts G1> and G1< (respectively) obey a simple proportionality relation that facilitates the introduction of a spectral weight function: It is also interpreted in terms of a periodicity/antiperiodicity property of a modified Green’s function in imaginary time capable of a Fourier series representation with imaginary (Matsubara) frequencies. The analytic continuation from imaginary time to real time is discussed, as are related commutator/anticommutator functions, also retarded/advanced Green’s functions, and the spectral weight sum rule is derived. Statistical thermodynamic information is shown to be embedded in physical features of the one- and two-particle thermodynamic Green’s functions.

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DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

Modern Physics Letters B ◽

10.1142/s021798490701244x ◽

2007 ◽

Vol 21 (02n03) ◽

pp. 139-154 ◽

Cited By ~ 6

Author(s):

J. H. ASAD

Keyword(s):

Differential Equation ◽

Green’S Function ◽

Recurrence Relation ◽

Green's Function ◽

Two Dimensional ◽

Dimensional Lattice ◽

One Dimensional ◽

The One ◽

Lattice Green's Function ◽

Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

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