scholarly journals Self-consistent ac quantum transport using nonequilibrium Green functions

2010 ◽  
Vol 81 (11) ◽  
Author(s):  
Diego Kienle ◽  
Mani Vaidyanathan ◽  
François Léonard
Keyword(s):  
Quantum Transport ◽  
Green Functions ◽  
Self Consistent ◽  
Nonequilibrium Green Functions

Many-body Green functions in nuclear physics

2017 ◽  
Vol 26 (01n02) ◽  
pp. 1740025 ◽  
Author(s):  
J. Speth ◽  
N. Lyutorovich
Keyword(s):  
Nuclear Physics ◽  
Green Functions ◽  
Many Body ◽  
General Applicability ◽  
Pair Correlations ◽  
Self Consistent ◽  
The Many ◽  
The One ◽  
General Relations ◽  
Three Body

Many-body Green functions are a very efficient formulation of the many-body problem. We review the application of this method to nuclear physics problems. The formulas which can be derived are of general applicability, e.g., in self-consistent as well as in nonself-consistent calculations. With the help of the Landau renormalization, one obtains relations without any approximations. This allows to apply conservation laws which lead to important general relations. We investigate the one-body and two-body Green functions as well as the three-body Green function and discuss their connection to nuclear observables. The generalization to systems with pair correlations are also presented. Numerical examples are compared with experimental data.

scholarly journals Self-Consistent Calculation of Particle-Hole Diagrams on the Matsubara Frequency: Flex Approximation

1997 ◽  
Vol 08 (05) ◽  
pp. 1145-1158
Author(s):  
J. J. Rodríguez-Núñez ◽  
S. Schafroth
Keyword(s):  
Hubbard Model ◽  
Imaginary Part ◽  
Chemical Potential ◽  
Order Approximation ◽  
The Self ◽  
Green Functions ◽  
Matsubara Frequency ◽  
Self Energy ◽  
Peak Structure ◽  
Self Consistent

We implement the numerical method of summing Green function diagrams on the Matsubara frequency axis for the fluctuation exchange (FLEX) approximation. Our method has previously been applied to the attractive Hubbard model for low density. Here we apply our numerical algorithm to the Hubbard model close to half filling (ρ =0.40), and for T/t = 0.03, in order to study the dynamics of one- and two-particle Green functions. For the values of the chosen parameters we see the formation of three branches which we associate with the two-peak structure in the imaginary part of the self-energy. From the imaginary part of the self-energy we conclude that our system is a Fermi liquid (for the temperature investigated here), since Im Σ( k , ω) ≈ w2 around the chemical potential. We have compared our fully self-consistent FLEX solutions with a lower order approximation where the internal Green functions are approximated by free Green functions. These two approches, i.e., the fully self-consistent and the non-self-consistent ones give different results for the parameters considered here. However, they have similar global results for small densities.

Nonlinear Elastic Properties of Micro-Heterogeneous Media

1994 ◽  
Vol 116 (3) ◽  
pp. 325-330 ◽  
Author(s):  
E. Kro¨ner
Keyword(s):  
Statistical Methods ◽  
Elastic Constants ◽  
Linear Elasticity ◽  
Heterogeneous Media ◽  
Nonlinear Problems ◽  
The Self ◽  
Green Functions ◽  
First Approximation ◽  
Self Consistent ◽  
Nonlinear Elastic

Utilizing statistical methods known from linear elasticity it is shown how effective 3rd (and higher) order elastic constants (TOEC) of micro-heterogeneous media can be calculated. Emphasis is put on the self consistent scheme. The ensemble average of the fluctuating TOEC yields a 0th approximation to the rigorous selfconsistent moduli. A first approximation is also given in closed form. The insight that the well-established statistical methods of the linear theory, which uses Green functions, are applicable also to nonlinear problems is considered as the main result of this paper.

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