Exactly Solvable Pairing in a Mean-field Framework: Models and Applications

2017 ◽  
pp. 327-355
Author(s):  
Feng Pan ◽  
Xin Guan ◽  
Jerry P. Draayer
Keyword(s):  
Mean Field ◽  
Exactly Solvable ◽  
Solvable Pairing

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.

Approximate Solutions

2020 ◽  
pp. 106-158
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Random Walk ◽  
Mean Field ◽  
Gaussian Model ◽  
Spherical Model ◽  
Approximate Solutions ◽  
Field Approximation ◽  
Approximation Schemes ◽  
Mean Field Approximation ◽  
Exactly Solvable ◽  
The Subject

Chapter 3 discusses the approximation schemes used to approach lattice statistical models that are not exactly solvable. In addition to the mean field approximation, it also considers the Bethe–Peierls approach to the Ising model. Moreover, there is a thorough discussion of the Gaussian model and its spherical version, both of which are two important systems with several points of interest. A chapter appendix provides a detailed analysis of the random walk on different lattices: apart from the importance of the subject on its own, it explains how the random walk is responsible for the critical properties of the spherical model.

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

scholarly journals Mean-field evolution of open quantum systems: an exactly solvable model

2012 ◽  
Vol 468 (2147) ◽  
pp. 3398-3412 ◽  
Author(s):  
M. Merkli ◽  
G. P. Berman
Keyword(s):  
Particle Number ◽  
Open Quantum Systems ◽  
Mean Field ◽  
Solvable Model ◽  
Direct Interaction ◽  
Quantum Particles ◽  
Exactly Solvable ◽  
Energy Conserving ◽  
Markovian Approximations ◽  
The Mean

We consider quantum particles coupled to local and collective thermal quantum environments. The coupling is energy conserving, and the collective coupling is scaled in the mean-field way. There is no direct interaction between the particles. We show that an initially factorized state of the particles remains factorized at all times, in the limit of large particle number. Each single-particle factor evolves according to an explicit, nonlinear, dissipative and time-dependent Hartree–Lindblad equation. The model is exactly solvable; we do not make any weak coupling or any Markovian approximations, and our results are mathematically rigorous.

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.

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