Two-Parameter Deformed SUSY Algebra for Fibonacci Oscillators

Abstract

We construct a two-parameter deformed SUSY algebra for the system of n ordinary fermions and n(q 1 , q 2 )-deformed bosons called Fibonacci oscillators with SU q 1 /q 2 (n)-symmetry. We then analyze the Fock space representation of the algebra constructed. We obtain the total deformed Hamiltonian and the energy levels together with their degeneracies for the system. We also consider some physical applications of the Fibonacci oscillators with SU q 1 /q 2 (n)-symmetry, and discuss the main reasons to consider two distinct deformation parameters.

A q-deformed particle algebra with a unique d-dimensional representation

“…These would be similar to two parameter [27,28] generalizations of the -oscillator which turn out to be important for thermodynamics [29,30].…”

Non-extensive entropy of bosonic Fibonacci oscillators

“…Although the role of quantum group invariance in non-extensive quantum statistical mechanics has been studied by means of the one-parameter quantum group structures [80,81], it has been argued in [17][18][19][20][21][22][23][24][25][34][35][36][37][38]43,65] that the two-parameter quantum group boson gas studies could give different consequences of thermostatistics.…”

Bose–Einstein condensation in a gas of Fibonacci oscillators

“…, , ( l n l q q n l q q x q q x q q n q q n l z q l z q q q q e z q e z q q dx x n z q q g (43) where…”

“…On the other hand, the second group of reasons comes originally from the phenomenological studies [43,44]. (i) The quantum algebra with two deformation parameters may have more flexibility when dealing with application to the concrete physical models [45].…”

“…For instance, it was shown in [42] that the quantum algebraic structure of the spin -1/2 XXZ chain with twisted periodic boundary conditions is a two-parameter deformed algebra ) 2 ( ,t q SU . On the other hand, the second group of reasons comes originally from the phenomenological studies [ 43,44]: (i) The quantum algebra with two deformation parameters may have more flexibility when dealing with application t o the concrete physical models [45]. Although any quantum algebra with one or more deformation parameters may be mapped onto the standard single -parameter case [46,47], the physical results obtained from a ( p,q)-deformed oscillator system are not the same.…”