The A-body exactly solvable pairing interaction from an engineering point of view

2020 ◽  
Author(s):  
V. G. Gueorguiev
Keyword(s):  
Point Of View ◽  
Pairing Interaction ◽  
Exactly Solvable ◽  
Solvable Pairing

scholarly journals Interaction between Different Kinds of Quantum Phase Transitions

2021 ◽  
Vol 3 (2) ◽  
pp. 253-261
Author(s):  
Angel Ricardo Plastino ◽  
Gustavo Luis Ferri ◽  
Angelo Plastino
Keyword(s):  
Phase Transitions ◽  
Nuclear Physics ◽  
Body Problem ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Many Body ◽  
Pairing Interaction ◽  
Exactly Solvable

We employ two different Lipkin-like, exactly solvable models so as to display features of the competition between different fermion–fermion quantum interactions (at finite temperatures). One of our two interactions mimics the pairing interaction responsible for superconductivity. The other interaction is a monopole one that resembles the so-called quadrupole one, much used in nuclear physics as a residual interaction. The pairing versus monopole effects here observed afford for some interesting insights into the intricacies of the quantum many body problem, in particular with regards to so-called quantum phase transitions (strictly, level crossings).

BETHE ANSATZ FOR NON-COMPACT GROUPS: THE PAIRING MODELS FOR BOSONS

2003 ◽  
Vol 17 (26) ◽  
pp. 1353-1363
Author(s):  
A. A. OVCHINNIKOV
Keyword(s):  
Bethe Ansatz ◽  
Transfer Matrix ◽  
Inverse Scattering Method ◽  
Compact Groups ◽  
Scattering Method ◽  
Helium Nanodroplets ◽  
New Class ◽  
Quasiclassical Limit ◽  
Exactly Solvable ◽  
Solvable Pairing

We discuss the construction of the exactly solvable pairing models for bosons in the framework of the Quantum Inverse Scattering method. It is stressed that this class of models naturally appears in the quasiclassical limit of the algebraic Bethe ansatz transfer matrix. We propose the new pairing Hamiltonians for bosons, depending on the additional parameters. It is pointed out that the new class of the pairing models can be obtained from the fundamental transfer-matrix. The possible new application of the pairing models for confined bosons in the physics of helium nanodroplets is pointed out.

scholarly journals EXACTLY SOLVABLE PAIRING MODEL USING AN EXTENSION OF THE RICHARDSON–GAUDIN APPROACH

2005 ◽  
Vol 14 (01) ◽  
pp. 47-55 ◽  
Author(s):  
A. B. BALANTEKIN ◽  
T. DERELI ◽  
Y. PEHLIVAN
Keyword(s):  
Energy Eigenstates ◽  
Energy Eigenvalues ◽  
New Class ◽  
Exactly Solvable ◽  
Sutherland Model ◽  
Pairing Model ◽  
Analytical Expressions ◽  
Solvable Pairing

We introduce a new class of exactly solvable boson pairing models using the technique of Richardson and Gaudin. Analytical expressions for all energy eigenvalues and the first few energy eigenstates are given. In addition, another solution to Gaudin's equation is also mentioned. A relation with the Calogero–Sutherland model is suggested.

RANK-TWO RICHARDSON-GAUDIN MODELS

2006 ◽  
Vol 15 (08) ◽  
pp. 1665-1679
Author(s):  
J. DUKELSKY ◽  
S. LERMA H. ◽  
B. ERREA ◽  
S. PITTEL ◽  
S. DIMITROVA ◽  
...  
Keyword(s):  
Nuclear Structure ◽  
Exactly Solvable ◽  
New Models ◽  
Gaudin Models ◽  
Solvable Pairing

We first review the development of the Richardson-Gaudin exactly-solvable pairing models and then discuss several new models based on rank-two algebras and their applications to problems in nuclear structure.

scholarly journals Exactly solvable pairing Hamiltonian for heavy nuclei

2011 ◽  
Vol 84 (6) ◽  
Author(s):  
J. Dukelsky ◽  
S. Lerma H. ◽  
L. M. Robledo ◽  
R. Rodriguez-Guzman ◽  
S. M. A. Rombouts
Keyword(s):  
Heavy Nuclei ◽  
Exactly Solvable ◽  
Solvable Pairing

EXACTLY SOLVABLE PAIRING HAMILTONIANS

2007 ◽  
Vol 16 (02) ◽  
pp. 210-221 ◽  
Author(s):  
J. DUKELSKY ◽  
B. ERREA ◽  
S. LERMA H. ◽  
S. PITTEL
Keyword(s):  
Exact Solution ◽  
Bcs Theory ◽  
Exactly Solvable ◽  
Theory Of Superconductivity ◽  
Solvable Pairing

We review the development of the microscopic BCS theory of superconductivity and the exact solution of the pairing Hamiltonian given by Richardson in 1963. We then introduce the generalized Richardson-Gaudin exactly-solvable pairing models for SU(2) (pairing between like particles), SO(5) ( T =1 pairing) and SO(8) ( T =0,1 pairing) algebras.

scholarly journals Class of Exactly Solvable Pairing Models

2001 ◽  
Vol 87 (6) ◽  
Author(s):  
J. Dukelsky ◽  
C. Esebbag ◽  
P. Schuck
Keyword(s):  
Exactly Solvable ◽  
Solvable Pairing
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