The description of collective motions in terms of many-body perturbation theory

1957 ◽  
Vol 240 (1223) ◽  
pp. 539-560 ◽  
Keyword(s):  
Collective Motion ◽  
Electron Plasma ◽  
Perturbation Series ◽  
Many Body ◽  
Self Energy ◽  
Collective Motions ◽  
Many Body Perturbation Theory ◽  
Set Up ◽  
The Many ◽  
Diagrammatic Method

In this and a succeeding paper it is shown how a theory equivalent to the Bohm & Pines collective motion theory of the electron plasma can be derived directly from a perturbation series which gives in principle an exact solution of the many-body problem. This result is attained by making use of a diagrammatic method of analysis of the perturbation series. By a process analogous to the elimination of photon self-energy parts from the electrodynamic S matrix it is found possible to simplify the perturbation series, introducing a modified interaction between the particles. A useful integral equation for this modified interaction can be set up, and it is shown how the energy of the system can be expressed in terms of the modified interaction. The close connexion between this approach and the dielectric theory of plasma oscillations is indicated.

scholarly journals Many-Electron QED with Redefined Vacuum Approach

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1014
Author(s):  
Romain N. Soguel ◽  
Andrey V. Volotka ◽  
Dmitry A. Glazov ◽  
Stephan Fritzsche
Keyword(s):  
Perturbation Theory ◽  
Electronic Configuration ◽  
Bound State ◽  
Many Body ◽  
Photon Exchange ◽  
Self Energy ◽  
Many Body Perturbation Theory ◽  
Formula Derivation ◽  
The Many ◽  
The One

The redefined vacuum approach, which is frequently employed in the many-body perturbation theory, proved to be a powerful tool for formula derivation. Here, we elaborate this approach within the bound-state QED perturbation theory. In addition to general formulation, we consider the particular example of a single particle (electron or vacancy) excitation with respect to the redefined vacuum. Starting with simple one-electron QED diagrams, we deduce first- and second-order many-electron contributions: screened self-energy, screened vacuum polarization, one-photon exchange, and two-photon exchange. The redefined vacuum approach provides a straightforward and streamlined derivation and facilitates its application to any electronic configuration. Moreover, based on the gauge invariance of the one-electron diagrams, we can identify various gauge-invariant subsets within derived many-electron QED contributions.

scholarly journals Many-Electron QED with Redefined Vacuum Approach

2021 ◽  
Author(s):  
Romain N. Soguel ◽  
Andrey V. Volotka ◽  
Dmitry A. Glazov ◽  
Stephan Fritzsche
Keyword(s):  
Perturbation Theory ◽  
Electronic Configuration ◽  
Bound State ◽  
Many Body ◽  
Photon Exchange ◽  
Self Energy ◽  
Many Body Perturbation Theory ◽  
Formula Derivation ◽  
The Many ◽  
The One

The redefined vacuum approach, which is frequently employed in the many-body perturbation theory, proved to be a powerful tool for formula derivation. Here, we elaborate this approach within the bound-state QED perturbation theory. In addition to general formulation, we consider the particular example of a single particle (electron or vacancy) excitation with respect to the redefined vacuum. Starting with simple one-electron QED diagrams, we deduce first- and second-order many-electron contributions: screened self-energy, screened vacuum polarization, one-photon exchange, and two-photon exchange. The redefined vacuum approach provides a straightforward and streamlined derivation and facilitates its application to any electronic configuration. Moreover, based on the gauge invariance of the one-electron diagrams, we can identify various gauge-invariant subsets within derived many-electron QED contributions.

scholarly journals Surface chemistry effects on work function, ionization potential and electronic affinity of Si(100), Ge(100) surfaces and SiGe heterostructures

2020 ◽  
Vol 22 (44) ◽  
pp. 25593-25605
Author(s):  
Ivan Marri ◽  
Michele Amato ◽  
Matteo Bertocchi ◽  
Andrea Ferretti ◽  
Daniele Varsano ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Surface Chemistry ◽  
Work Function ◽  
Ionization Potential ◽  
Many Body ◽  
Many Body Perturbation Theory ◽  
The Many ◽  
Electronic Affinity

Surface chemistry effects are calculated within the many body perturbation theory for Si(100), Ge(100) and SiGe surfaces.

scholarly journals Many-body effects in semiconducting single-wall silicon nanotubes

2014 ◽  
Vol 5 ◽  
pp. 19-25 ◽  
Author(s):  
Wei Wei ◽  
Timo Jacob
Keyword(s):  
Binding Energies ◽  
Band Gaps ◽  
Many Body ◽  
Nanoscale Device ◽  
Strong Electron ◽  
Self Energy ◽  
Silicon Nanotubes ◽  
Particle Level ◽  
The Many ◽  
Silicon Based

The electronic and optical properties of semiconducting silicon nanotubes (SiNTs) are studied by means of the many-body Green’s function method, i.e., GW approximation and Bethe–Salpeter equation. In these studied structures, i.e., (4,4), (6,6) and (10,0) SiNTs, self-energy effects are enhanced giving rise to large quasi-particle (QP) band gaps due to the confinement effect. The strong electron−electron (e−e) correlations broaden the band gaps of the studied SiNTs from 0.65, 0.28 and 0.05 eV at DFT level to 1.9, 1.22 and 0.79 eV at GW level. The Coulomb electron−hole (e−h) interactions significantly modify optical absorption properties obtained at noninteracting-particle level with the formation of bound excitons with considerable binding energies (of the order of 1 eV) assigned: the binding energies of the armchair (4,4), (6,6) and zigzag (10,0) SiNTs are 0.92, 1.1 and 0.6 eV, respectively. Results in this work are useful for understanding the physics and applications in silicon-based nanoscale device components.

The calculation of higher-order energies in the many-body perturbation theory series

1985 ◽  
Vol 113 (1) ◽  
pp. 8-12 ◽  
Author(s):  
P.J. Knowles ◽  
K. Somasundram ◽  
N.C. Handy ◽  
K. Hirao
Keyword(s):  
Perturbation Theory ◽  
Higher Order ◽  
Many Body ◽  
Many Body Perturbation Theory ◽  
The Many ◽  
Theory Series

Towards numerical implementation of the relativistically covariant many-body perturbation theoryThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at University of Windsor, Windsor, Ontario, Canada on 21–26 July 2008.

2009 ◽  
Vol 87 (7) ◽  
pp. 817-824 ◽  
Author(s):  
Daniel Hedendahl ◽  
Ingvar Lindgren ◽  
Sten Salomonson
Keyword(s):  
Standard Procedure ◽  
Operator Method ◽  
Vertex Correction ◽  
Many Body ◽  
Atomic Systems ◽  
Self Energy ◽  
Electron Positron ◽  
Many Body Perturbation Theory ◽  
Qed Effects ◽  
First Time

The standard procedure for relativistic many-body perturbation theory (RMBPT) is not relativistically covariant, and the effects of retardation, virtual-electron-positron-pair, and radiative effects (self-energy, vacuum polarisation, and vertex correction) — the so-called QED effects — are left out. The energy contribution from the QED effects can be evaluated by the covariant evolution operator method, which has a structure that is similar to that of RMBPT, and it can serve as a merger between QED and RMBPT. The new procedure makes it, in principle, possible for the first time to evaluate QED effects together with correlation to high order. The procedure is now being implemented, and it has been shown that the effect of electron correlation on first-order QED for He-like neon dominates heavily over second-order QED effects.

scholarly journals Design of auxiliary systems for spectroscopy

2020 ◽  
Vol 224 ◽  
pp. 424-447
Author(s):  
Marco Vanzini ◽  
Francesco Sottile ◽  
Igor Reshetnyak ◽  
Sergio Ciuchi ◽  
Lucia Reining ◽  
...  
Keyword(s):  
Spectral Properties ◽  
Density Functional ◽  
The Self ◽  
Many Body ◽  
Functional Theory ◽  
Correlation Kernel ◽  
Effective Potentials ◽  
Exchange Correlation ◽  
Self Energy ◽  
Many Body Perturbation Theory

In this contribution, we advocate the possibility of designing auxiliary systems with effective potentials or kernels that target only the specific spectral properties of interest and are simpler than the self-energy of many-body perturbation theory or the exchange–correlation kernel of time-dependent density-functional theory.

THE SCREENING FUNCTION OF AN INTERACTING ELECTRON GAS

1966 ◽  
Vol 44 (9) ◽  
pp. 2137-2171 ◽  
Author(s):  
D. J. W. Geldart ◽  
S. H. Vosko
Keyword(s):  
Electron Gas ◽  
Substantial Contribution ◽  
Fundamental Relation ◽  
Many Body ◽  
Screening Constant ◽  
Self Energy ◽  
Self Consistent ◽  
Small Wave ◽  
Many Body Perturbation Theory ◽  
Zero Frequency

The screening function of an interacting electron gas at high and metallic densities is investigated by many-body perturbation theory. The analysis is guided by a fundamental relation between the compressibility of the system and the zero-frequency small wave-vector screening function (i.e. screening constant). It is shown that the contribution from a graph not included in previous work is essential to obtain the lowest-order correlation correction to the screening constant at high density. Also, this graph gives a substantial contribution to the screening constant at metallic densities. The general problem of choosing a self-consistent set of graphs for calculating the screening function is discussed in terms of a coupled set of integral equations for the propagator, the self-energy, the vertex function, and the screening function. A modification of Hubbard's (1957) form of the screening function is put forward on the basis of these results.

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