scholarly journals Exact calculation of the ground‐state single‐particle Green’s function for the 1/r2 quantum many‐body system at integer coupling

1995 ◽  
Vol 36 (1) ◽  
pp. 86-96 ◽  
Author(s):  
P. J. Forrester
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Single Particle ◽  
Ground State ◽  
Exact Calculation ◽  
Body System ◽  
Many Body

scholarly journals Pole skipping and chaos in anisotropic plasma: a holographic study

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Karunava Sil
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Complex Frequency ◽  
Body System ◽  
Many Body ◽  
Sound Channel ◽  
Spatial Anisotropy ◽  
Momentum Plane ◽  
Upper Half Plane ◽  
Holographic Study

Abstract Recently, a direct signature of chaos in many body system has been realized from the energy density retarded Green’s function using the phenomenon of ‘pole skipping’. Moreover, special locations in the complex frequency and momentum plane are found, known as the pole skipping points such that the retarded Green’s function can not be defined uniquely there. In this paper, we compute the correction/shift to the pole skipping points due to a spatial anisotropy in a holographic system by performing near horizon analysis of EOMs involving different bulk field perturbations, namely the scalar, the axion and the metric field. For vector and scalar modes of metric perturbations we construct the gauge invariant variable in order to obtain the master equation. Two separate cases for every bulk field EOMs is considered with the fluctuation propagating parallel and perpendicular to the direction of anisotropy. We compute the dispersion relation for momentum diffusion along the transverse direction in the shear channel and show that it passes through the first three successive pole skipping points. The pole skipping phenomenon in the sound channel is found to occur in the upper half plane such that the parameters Lyapunov exponent λL and the butterfly velocity vB are explicitly obtained thus establishing the connection with many body chaos.

AN INTRODUCTORY GUIDE TO GREEN’S FUNCTION METHODS IN NUCLEAR MANY-BODY PROBLEMS

1994 ◽  
Vol 03 (02) ◽  
pp. 523-589 ◽  
Author(s):  
T.T.S. KUO ◽  
YIHARN TZENG
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Model Space ◽  
Many Body ◽  
Diagram Expansion ◽  
Nucleus Scattering ◽  
Many Body Systems ◽  
General Method

We present an elementary and fairly detailed review of several Green’s function methods for treating nuclear and other many-body systems. We first treat the single-particle Green’s function, by way of which some details concerning linked diagram expansion, rules for evaluating Green’s function diagrams and solution of the Dyson’s integral equation for Green’s function are exhibited. The particle-particle hole-hole (pphh) Green’s function is then considered, and a specific time-blocking technique is discussed. This technique enables us to have a one-frequency Dyson’s equation for the pphh and similarly for other Green’s functions, thus considerably facilitating their calculation. A third type of Green’s function considered is the particle-hole Green’s function. RPA and high order RPA are treated, along with examples for setting up particle-hole RPA equations. A general method for deriving a model-space Dyson’s equation for Green’s functions is discussed. We also discuss a method for determining the normalization of Green’s function transition amplitudes based on its vertex function. Some applications of Green’s function methods to nuclear structure and recent deep inelastic lepton-nucleus scattering are addressed.

Eine Approximation der Löwdinschen natürlichen Orbitale für Moleküle mit einer Green-Funktion-Methode

1972 ◽  
Vol 27 (4) ◽  
pp. 545-552 ◽  
Author(s):  
R. Albat
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Mass Operator ◽  
Ground States ◽  
Present Form ◽  
Many Body ◽  
Natural Orbitals ◽  
First Order ◽  
The Many ◽  
Closed Shells

Abstract An Approximation of Löwdin's Natural Orbitals for Molecules with a Green's Function Method The many-body-pertubation theorie of the single-particle Green's function is used to get an approximate first-order density matrix. Slightly modified SCF-orbitals form the basis for the expansion. The mass-operator in Dyson's equation is considered up to second order in the Perturbation. In the present form the method is only applicable to ground states with closed shells. The ground states of the molecules LiH and NH3 serve as examples to demonstrate the usefulness of the directly calculated natural orbitals for application in the C I-method. The natural orbitals give a much better convergence of the C I-expansion than the SCF-orbitals do.

Mesonic and isobar degrees of freedom in the ground state of the nuclear many-body system

1978 ◽  
Vol 18 (5) ◽  
pp. 2416-2429 ◽  
Author(s):  
M. R. Anastasio ◽  
Amand Faessler ◽  
H. Müther ◽  
K. Holinde ◽  
R. Machleidt
Keyword(s):  
Ground State ◽  
Degrees Of Freedom ◽  
Body System ◽  
Many Body
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