The q-Deformed Versions of the Pairing Interaction

J.-z. Zhang, P. Osland

Sidney S. Avancini, Débora Peres Menezes

We investigate the behaviour of the pairing model within the context of quantum algebras. The pairing Hamiltonian is diagonalized exactly for different values of the deformation parameter q in systems with 8 and 50 particles. The same Hamiltonian is solved with the help of the coherent state variational method. We find that the variational method gives reliable results when compared with the exact ones. We also discuss the differences between the two deformation procedures.

Wachter, Hartmut

We develop a formalism for the scattering of a particle on the $q$-deformed Euclidean space. We write down $q$-versions of the Lippmann-Schwinger equation. Their iterative solutions for a weak scattering potential lead us to $q$-versions of the Born series. With the expressions for the wave functions of the scattered particle, we can write down S-matrix elements. We show that these S-matrix elements satisfy unitarity conditions. Considerations about the interaction picture for a quantum system in the $q$-deformed Euclidean space and a discussion of a $q$-version of time-dependent perturbation theory conclude our studies.

F.J.W. Hahne, Peter A. Ring

R. N. Alvarez, Dennis Bonatsos A, Yu.F. Smirnov

A deformed version of the vibron model for diatomic molecules is constructed. Both the O(4) and U(3) dynamical symmetries of the model are rewritten, using the concept of complementary subalgebras, in a more convenient form, which is subsequently deformed. The present model unifies the so far independent successful quantum-algebraic approaches to rotational and to vibrational spectra of diatomic molecules. In addition, the method can be used for the construction of deformed versions of the U(5) and O(6) limits of the interacting boson model of nuclear structure.

P. Narayana Swamy