scholarly journals Exactly and Quasi-Exactly Solvable Models on the Basis of OSP(2|1)

1997 ◽  
Vol 12 (22) ◽  
pp. 1655-1661
Author(s):  
A. Shafiekhani ◽  
M. Khorrami
Keyword(s):  
Symmetry Algebra ◽  
Dynamical Symmetry ◽  
One Dimension ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Exactly Solvable ◽  
Solvable Problems

The exactly and quasi-exactly solvable problems for spin one-half in one dimension on the basis of a hidden dynamical symmetry algebra of Hamiltonian are discussed. We take the supergroup, OSP(2|1), as such a symmetry. A number of exactly solvable examples are considered and their spectrum are evaluated explicitly. Also, a class of quasi-exactly solvable problems on the basis of such a symmetry has been obtained.

QUASI-EXACTLY SOLVABLE PROBLEMS AND SU(1,1) GROUP

1994 ◽  
Vol 09 (16) ◽  
pp. 1501-1505 ◽  
Author(s):  
O.B. ZASLAVSKII
Keyword(s):  
Lie Algebra ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Dimensional Representation ◽  
One Dimensional ◽  
Infinite Dimensional ◽  
Exactly Solvable ◽  
Solvable Problems ◽  
Infinite Dimensional Representation

It is shown that the particular class of one-dimensional quasi-exactly solvable models can be constructed with the help of infinite-dimensional representation of Lie algebra. Hamiltonian of a system is expressed in terms of SU(1,1) generators.

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).

scholarly journals Exactly solvable models in arbitrary dimensions

1998 ◽  
Vol 238 (4-5) ◽  
pp. 213-218 ◽  
Author(s):  
Ranjan Kumar Ghosh ◽  
Sumathi Rao
Keyword(s):  
Exactly Solvable Models ◽  
Solvable Models ◽  
Exactly Solvable ◽  
Arbitrary Dimensions

Exactly solvable models for trapped boson systems

2004 ◽  
Vol 243 (1-6) ◽  
pp. 131-143 ◽  
Author(s):  
J. Dukelsky ◽  
G.G. Dussel ◽  
S. Pittel
Keyword(s):  
Exactly Solvable Models ◽  
Solvable Models ◽  
Boson Systems ◽  
Exactly Solvable

scholarly journals Exactly solvable models through the empty-interval method

2001 ◽  
Vol 64 (5) ◽  
Author(s):  
M. Alimohammadi ◽  
M. Khorrami ◽  
A. Aghamohammadi
Keyword(s):  
Exactly Solvable Models ◽  
Solvable Models ◽  
Empty Interval ◽  
Interval Method ◽  
Exactly Solvable
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