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Communications in Physics

On Generalized q-deformed Fermionic Oscillators

Luu Thi Kim Thanh

Published Jul 18, 2008• 0 citations
Publisher

Abstract

In this work we consider a version of generalized q-deformed fermionic oscillators and some their applications. The corresponding coherent states are constructed. The statistical distribution of generalized q-deformed fermionic oscillators system, expressions for quadrature variances and the average particle number in the coherent states are calculated.

DOI
10.15625/0868-3166/18/1/10686

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In this work we consider a version of generalized q-deformed fermionic oscillators and some their applications. The corresponding coherent states are constructed. The statistical distribution of generalized q-deformed fermionic oscillators system, expressions for quadrature variances and the average particle number in the coherent states are calculated.
Abstract The theory of q -deformed fermions is one of the theories of q -deformed oscillators. Within the framework of this theory and the traditional fluctuation theory, we investigate fluctuations of q -deformed fermion gas and obtain the expressions of fluctuations of the internal energy U , the particle number N and the correlation of fluctuations of the two physical quantities above. Further numerical calculation reveals that fluctuations of such a system have some interesting and particular features. We consider that this work may provide much insight into the theory of q fermions, and may also be helpful for the theory of q -deformed oscillators.
By making use of the Fock States of the q-deformed quantum oscillator which possesses the symmetry of quantum group, we construct the Glauber coherent state of the q-deformed quantum oscillator (the q-Glauber coherent state ㄧα>q). We discuss the of completeness properties, particle number distribution, oscillator strength distribution and the minimal uncertainty principle of the q-Glauber coherent states, and point out that the coherent degree of the q-Glauber coherent state can be described by the parameter q.
Adopting the framework of the generalized q -deformed Heisenberg–Weyl algebra , we present a mathematical procedure which leads us to obtain analytical expressions for a general class of q -deformed coherent states associated with the different patterns of the energy spectrum exhibited by the nonlinear f -oscillator. In particular, we establish the properties of a small group of q -deformed coherent states for α > γ > 0 with emphasis on the resolution of unity. As an application of these properties, we investigate the Robertson–Schrödinger uncertainty relation and the squeezing effect for the deformed coordinate and momentum operators, which are defined in terms of the abstract elements of this algebra. Furthermore, we also obtain the Wigner function and the correct quantum-mechanical marginal distributions in phase space.