Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximation

2017 ◽  
Author(s):  
J. Terasaki ◽  
A. Smetana ◽  
F. Šimkovic ◽  
M. I. Krivoruchenko
Keyword(s):  
Exact Solutions ◽  
Random Phase Approximation ◽  
Random Phase ◽  
Phase Approximation ◽  
Lipkin Model

scholarly journals Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximation

2017 ◽  
Vol 26 (10) ◽  
pp. 1750062 ◽  
Author(s):  
J. Terasaki ◽  
A. Smetana ◽  
F. Šimkovic ◽  
M. I. Krivoruchenko
Keyword(s):  
Exact Solutions ◽  
Excited States ◽  
Random Phase Approximation ◽  
Particle Number ◽  
Random Phase ◽  
Creation Operator ◽  
Phase Approximation ◽  
Many Body ◽  
Lipkin Model ◽  
Number Formula

It is shown that the random-phase approximation (RPA) method with its nonlinear higher generalization, which was previously considered as approximation except for a very limited case, reproduces the exact solutions of the Lipkin model. The nonlinear higher RPA is based on an equation nonlinear on eigenvectors and includes many particle-many hole components in the creation operator of the excited states. We demonstrate the exact character of solutions analytically for the particle number [Formula: see text] and, numerically, for [Formula: see text]. This finding indicates that the nonlinear higher RPA is equivalent to the exact Schrödinger equation, which opens up new possibilities for realistic calculations in many-body problems.

Application of the resonating Hartree-Fock random phase approximation to the Lipkin model

1996 ◽  
Vol 599 (3-4) ◽  
pp. 457-485 ◽  
Author(s):  
Seiya Nishiyama ◽  
Kazuhiro Ishida ◽  
Moriyoshi Ido
Keyword(s):  
Random Phase Approximation ◽  
Random Phase ◽  
Phase Approximation ◽  
Hartree Fock ◽  
Lipkin Model

Interpretation of Preferential Adsorption Using Random Phase Approximation Theory

1995 ◽  
Vol 60 (10) ◽  
pp. 1641-1652 ◽  
Author(s):  
Henri C. Benoît ◽  
Claude Strazielle
Keyword(s):  
Approximation Theory ◽  
Random Phase Approximation ◽  
Virial Coefficient ◽  
Random Phase ◽  
Second Virial Coefficient ◽  
Solvent Mixture ◽  
Gyration Radius ◽  
Thermodynamic Quantities ◽  
Phase Approximation ◽  
Preferential Adsorption

It has been shown that in light scattering experiments with polymers replacement of a solvent by a solvent mixture causes problems due to preferential adsorption of one of the solvents. The present paper extends this theory to be applicable to any angle of observation and any concentration by using the random phase approximation theory proposed by de Gennes. The corresponding formulas provide expressions for molecular weight, gyration radius, and the second virial coefficient, which enables measurements of these quantities provided enough information on molecular and thermodynamic quantities is available.

Neutrino reactions onC12by the quasiparticle random-phase approximation (QRPA)

2010 ◽  
Vol 81 (2) ◽  
Author(s):  
Myung-Ki Cheoun ◽  
Eunja Ha ◽  
Su Youn Lee ◽  
K. S. Kim ◽  
W. Y. So ◽  
...  
Keyword(s):  
Random Phase Approximation ◽  
Random Phase ◽  
Phase Approximation ◽  
Quasiparticle Random Phase Approximation
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