Selfenergy

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Correlation Functions ◽  
Doppler Shift ◽  
Secular Equation ◽  
Wave Functions ◽  
Local Velocity ◽  
Microscopic Picture ◽  
Quasiparticle Picture

The averaged wave functions allow defining the transport vertex. For the correlation functions this leads to the Generalised Kadanoff and Baym formalism with the Langreth–Wilkins rules. The meaning of the selfenergy is explored. The Green’s function is a secular equation in which the complicated motion of a particle during interaction is represented by the selfenergy. The quasiparticle picture is applicable to long trajectories, where the averaged velocity is of interest. In processes like emission, the Doppler shift depends on the local velocity and one has to return to the microscopic picture. The application scheme how to construct and use the selfenergy is presented.

Integral equations and relations for Lamé functions and ellipsoidal wave functions

1968 ◽  
Vol 64 (1) ◽  
pp. 113-126 ◽  
Author(s):  
B. D. Sleeman
Keyword(s):  
Wave Function ◽  
Green’S Function ◽  
Integral Equations ◽  
Green's Function ◽  
Function Theory ◽  
Natural Generalization ◽  
Wave Functions ◽  
Linear Integral ◽  
First Time ◽  
Linear Integral Equations

AbstractNon-linear integral equations and relations, whose nuclei in all cases is the ‘potential’ Green's function, satisfied by Lamé polynomials and Lamé functions of the second kind are discussed. For these functions certain techniques of analysis are described and these find their natural generalization in ellipsoidal wave-function theory. Here similar integral equations are constructed for ellipsoidal wave functions of the first and third kinds, the nucleus in each case now being the ‘free space’ Green's function. The presence of ellipsoidal wave functions of the second kind is noted for the first time. Certain possible generalizations of the techniques and ideas involved in this paper are also discussed.

scholarly journals The Use of Parameter-Free Correlation Functions in Green's Function Monte Carlo Simulations of Small Electronic Systems

1997 ◽  
Vol 52 (11) ◽  
pp. 793-802 ◽  
Author(s):  
C. Mecke ◽  
F. F. Seelig
Keyword(s):  
Monte Carlo ◽  
Green’S Function ◽  
Green's Function ◽  
Correlation Functions ◽  
High Performance ◽  
Limited Range ◽  
Electronic Energy ◽  
Simple Expression ◽  
Electronic Systems ◽  
Green's Function Monte Carlo

Abstract Using an old formulation for correlation functions with correct cusp-behaviour, the Schrödinger equation transforms to a new differential equation which provides a very simple expression for the local electronic energy with limited range. This, together with the simplicity of the formulation promises a high performance in Green's function Monte Carlo (GFMC) simulations of small electronic systems. The behaviour of the local energy is studied on a few simple examples because the variance of this function determines the quality of the results in the GFMC methods. Calculations for one-and two-electron systems are presented and compared with results from well-known functions. The form of the function is then extended to systems with more than two electrons. Results for the Be atom are given and the extension to larger electronic systems is discussed.

Operators of minimal norm via modified Green's functions

1983 ◽  
Vol 94 (1-2) ◽  
pp. 163-178 ◽  
Author(s):  
R. E. Kleinman ◽  
G. F. Roach
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Spherical Wave ◽  
Boundary Integral ◽  
Wave Functions ◽  
Constructive Method ◽  
Minimal Norm ◽  
Neumann Problems ◽  
Integral Equation Formulation ◽  
Method Of Solution

SynopsisThe exterior Dirichlet and Neumann problems can be treated very satisfactorily by using a fundamental solution which is modified by adding radiating spherical wave functions. It has been shown [3], that the coefficients of these added terms can be chosen to ensure that the associated boundary integral equation formulation of the problem was uniquely solvable and, in addition, that the modified Green's function was a least squares best approximation to the exact Green's function for the problem. Here we show that the coefficients can be chosen to ensure not only unique solvability but also minimization of the norm of the modified integral operator. This leads to a constructive method of solution. The theory is illustrated when the boundary is a sphere and when it is a perturbation of a sphere.

Particle with a time-dependent mass in the Coulomb and the inverse quadratic potentials

2018 ◽  
Vol 15 (04) ◽  
pp. 1850057
Author(s):  
Badri Berrabah ◽  
Baya Bentag ◽  
Ahmida Bendjoudi
Keyword(s):  
Charged Particle ◽  
Green’S Function ◽  
Green's Function ◽  
Bound States ◽  
Energy Levels ◽  
Wave Functions ◽  
Time Dependent ◽  
Quadratic Potentials ◽  
Dependent Mass

The problem of a spineless charged particle with a time-dependent decaying mass interacting with a Coulomb and an inverse quadratic potentials is considered. The Green’s function is explicitly evaluated. The energy levels as well as the wave functions for the bound states are exactly determined.

scholarly journals Forward-walking Green's Function Monte Carlo Method for Correlation Functions

1999 ◽  
Vol 52 (4) ◽  
pp. 637 ◽  
Author(s):  
M. Samaras ◽  
C. J. Hamer
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Green’S Function ◽  
Green's Function ◽  
Correlation Functions ◽  
Exact Results ◽  
Expectation Values ◽  
Trial Wavefunction ◽  
Local Observables ◽  
Green's Function Monte Carlo

The forward-walking Green's Function Monte Carlo method is used to compute expectation values for the transverse Ising model in (1 + 1)D, and the results are compared with exact values. The magnetisation Mz and the correlation function p z (n) are computed. The algorithm reproduces the exact results, and convergence for the correlation functions seems almost as rapid as for local observables such as the magnetisation. The results are found to be sensitive to the trial wavefunction, however, especially at the critical point.

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