Evaluation of correlation functions and wave-functions of the Gaussian random potentials by numerical shooting method

We aimed to evaluate the ground-state and excite-state energy eigenvalue (En), wave function, and the time-independent correlation function of the atomic density fluctuation of a particle under the harmonics oscillator Cosine asymmetric potential (Saad et al. 2013). Instead of using the 6-point kernel of 4 Green’s function (Cherroret and Skipetrov, 2008), averaged over disorder, we use the numerical shooting method (NSM) to solve the Schrödinger equation of quantum mechanics system with Cosine asymmetric potential. Since our approach does not use complicated formulas, it requires much less computational effort when compared to the Green functions techniques (Cherroret and Skipetrov, 2008). We show that the idea of the program of evaluating time-independent correlation function of atomic density is underdamped motion for the Cosine asymmetric potential from the numerical shooting method of this problem. Comparison of the time-independent correlation function obtained from numerical shooting method by Boonchui and Hutem (2012) and correlation function experiment by Kasprzak et al. (2008). We show the intensity of atomic density fluctuation (δn(x)=n~(x)-m~(x)) in harmonics oscillator Cosine asymmetric potential by numerical shooting method.

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On spectral properties of parton correlation functions and multiparton wave functions

Physics Letters B ◽

10.1016/0370-2693(83)91116-4 ◽

1983 ◽

Vol 131 (1-3) ◽

pp. 179-182 ◽

Cited By ~ 24

Author(s):

A.V. Radyushkin

Keyword(s):

Correlation Functions ◽

Spectral Properties ◽

Wave Functions

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Two-nucleon density functions and correlation functions with realistic single-particle wave functions

Nuclear Physics A ◽

10.1016/0375-9474(70)90695-0 ◽

1970 ◽

Vol 149 (2) ◽

pp. 261-272 ◽

Cited By ~ 2

Author(s):

Daphne F. Jackson ◽

S. Murugesu

Keyword(s):

Single Particle ◽

Correlation Functions ◽

Wave Functions ◽

Density Functions ◽

Nucleon Density

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Selfenergy

10.1093/oso/9780198797241.003.0006 ◽

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.

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Conformal group theory of tensor structures

Journal of High Energy Physics ◽

10.1007/jhep10(2020)004 ◽

2020 ◽

Vol 2020 (10) ◽

Cited By ~ 3

Author(s):

Ilija Burić ◽

Volker Schomerus ◽

Mikhail Isachenkov

Keyword(s):

Correlation Functions ◽

Conformal Group ◽

Wave Functions ◽

Dimensional Euclidean Space ◽

Theoretic Approach ◽

Conformal Blocks ◽

Conformal Field ◽

Local Operators ◽

Indispensable Tool ◽

Systematic Derivation

Abstract The decomposition of correlation functions into conformal blocks is an indispensable tool in conformal field theory. For spinning correlators, non-trivial tensor structures are needed to mediate between the conformal blocks, which are functions of cross ratios only, and the correlation functions that depend on insertion points in the d-dimensional Euclidean space. Here we develop an entirely group theoretic approach to tensor structures, based on the Cartan decomposition of the conformal group. It provides us with a new universal formula for tensor structures and thereby a systematic derivation of crossing equations. Our approach applies to a ‘gauge’ in which the conformal blocks are wave functions of Calogero-Sutherland models rather than solutions of the more standard Casimir equations. Through this ab initio construction of tensor structures we complete the Calogero-Sutherland approach to conformal correlators, at least for four-point functions of local operators in non-supersymmetric models. An extension to defects and superconformal symmetry is possible.

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