Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximation
- NázevTitle
- Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximationReproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximation
- Druh výsledkuResult type
- Článek v časopiseJournal article
- AutořiAuthors
- J. Terasaki, A. Smetana, F. Šimkovic, M. I. Krivoruchenko
- DOIDOI
- 10.1142/S0218301317500628
- Časopis / citaceJournal / citation
- International Journal of Modern Physics E. 2017, 26(10), ISSN 0218-3013.
- RokYear
- 2017
- JazykLanguage
- eng
- WoSWoS
- 000414572300004
- ScopusScopus
- 2-s2.0-85031796384
- RIVRIV
- RIV/68407700:21670/17:00318754!RIV18-MSM-21670___
- ProjektProject
- Podzemní laboratoř LSM - česká účast ve výzkumné infrastruktuře evropského významuUnderground laboratory LSM - Czech participation to European-level research infrastructure
AbstraktAbstract
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 N = 2 and, numerically, for N = 8. This finding indicates that the nonlinear higher RPA is equivalent to the exact Schrodinger equation, which opens up new possibilities for realistic calculations in many-body problems.
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 N = 2 and, numerically, for N = 8. This finding indicates that the nonlinear higher RPA is equivalent to the exact Schrodinger equation, which opens up new possibilities for realistic calculations in many-body problems.