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International Journal of Modern Physics E

Exact Dyson Expansion for a Single J-Shell Within the Quon Algebra

Sidney S. Avancini, José Ricardo Marinelli, Débora Peres Menezes, Mello Moraes, Naotaka Yoshinaga

Published Jun 1, 1998• 4 citations
Publisher

Abstract

The quon algebra, which interpolates between the Bose and Fermi algebras and depends on a free paramenter q, is used to generate a deformed Dyson boson expansion of the quadrupole operator. Then we obtain a quadrupole-quadrupole hamiltonian, for a single j-shell, in terms of this deformed bosonic operator. The hamiltonian is diagonalized and its eigenvalues are compared with the ones obtained from the fermionic quadrupole-quadrupole hamiltonian. The deformation parameter helps in achieving the correct excitation energy levels, what cannot be encountered in practice with the usual non-deformed Dyson expansion.

DOI
10.1142/s0218301398000178

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The quon algebra, which interpolates between the Bose and Fermi algebras and depends on a free paramenter q, is used to generate a deformed Dyson boson expansion of the quadrupole operator. Then we obtain a quadrupole-quadrupole hamiltonian, for a single j-shell, in terms of this deformed bosonic operator. The hamiltonian is diagonalized and its eigenvalues are compared with the ones obtained from the fermionic quadrupole-quadrupole hamiltonian. The deformation parameter helps in achieving the correct excitation energy levels, what cannot be encountered in practice with the usual non-deformed Dyson expansion.
The quon algebra, which interpolates between the Bose and Fermi algebras and depends on a free paramenter qqq, is used to generate a deformed Dyson boson expansion of the quadrupole operator. Then we obtain a quadrupole-quadrupole hamiltonian, for a single j-shell, in terms of this deformed bosonic operator. The hamiltonian is diagonalized and its eigenvalues are compared with the ones obtained from the fermionic quadrupole-quadrupole hamiltonian. The deformation parameter helps in achieving the correct energy levels, what cannot be encountered in practice with the usual non-deformed Dyson expansion.
The quon algebra, which interpolates between the Bose and Fermi algebras and depends on a free parameter q , is used to generate deformed Marumori boson expansions for the pair and quadrupole operators. Then we obtain a pairing plus quadrupole-quadrupole Hamiltonian, for a single j -shell, in terms of these deformed bosonic operators. The Hamiltonian is diagonalized and its eigenvalues are compared with the ones obtained from the counterpart fermionic Hamiltonian. The deformation parameter helps in achieving the correct energy levels, which cannot be encountered in practice with the usual non-deformed boson expansion.
The quon algebra, which interpolates between the Bose and Fermi algebras and depends on a free parameter q , is used to generate a Marumori mapping of the quadrupole-quadrupole Hamiltonian, for a single j -shell. This Hamiltonian is then diagonalized for a system composed of six fermions and its eigenvalues are compared with the ones obtained from the counterpart fermionic Hamiltonian and with another usual boson expansion method. The deformed mapping is shown to require a larger basis than the usual Marumori method for the diagonalization of the Hamiltonian. The low-lying levels of the spectrum obtained from the fermionic calculation in the SD subspace can be reproduced with our mapping for some selected j -shells.
The boson expansion method is applied to find the spectrum of a q-deformed harmonic oscillator. We use two different boson expansions, each of them including a deformation parameter, defined in terms of exponential and logarithmic functionals. The resulting Hamiltonians are bilinear forms of the transformed operators. Physical effects resulting from the deformation of the generators of the algebra are studied by comparing known finite-range potentials and the effective potentials obtained for each of the considered Hamiltonians.
Operators, refered to as k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of two noncommuting quon algebras. The deformation parameters for these quon algebras are roots of unity connected to an integer k. The case k=2 corresponds to fermions and the limiting case k going to infinity to bosons. Generalized coherent states and supercoherent states are investigated. The Dirac quantum phase operator and the Fairlie-Fletcher-Zachos algebra are also considered.