Abdullah Algin

Bose–Einstein condensation in a gas of Fibonacci oscillators

We consider a system of two-parameter deformed boson oscillators whose spectrum is given by a generalized Fibonacci sequence. In order to establish the role of the deformation parameters (q1,q2) in the thermostatistics of the system, we calculate several thermostatistical functions in the thermodynamical limit and investigate the low temperature behavior of the system. In this framework, we show that the thermostatistics of the (q1,q2)-bosons can be studied using the formalism of Fibonacci calculus which generalizes the recently proposed formalism of q-calculus. We also discuss the conditions under which the Bose–Einstein condensation would occur in the present two-parameter generalized boson gas. However, the ordinary boson gas results can be obtained by applying the limit q1 = q2 = 1.

High temperature behavior of a deformed Fermi gas obeying interpolating statistics

An outstanding idea originally introduced by Greenberg is to investigate whether there is equivalence between intermediate statistics, which may be different from anyonic statistics, and q-deformed particle algebra. Also, a model to be studied for addressing such an idea could possibly provide us some new consequences about the interactions of particles as well as their internal structures. Motivated mainly by this idea, in this work, we consider a q-deformed Fermi gas model whose statistical properties enable us to effectively study interpolating statistics. Starting with a generalized Fermi-Dirac distribution function, we derive several thermostatistical functions of a gas of these deformed fermions in the thermodynamical limit. We study the high-temperature behavior of the system by analyzing the effects of q deformation on the most important thermostatistical characteristics of the system such as the entropy, specific heat, and equation of state. It is shown that such a deformed fermion model in two and three spatial dimensions exhibits the interpolating statistics in a specific interval of the model deformation parameter 0 < q < 1. In particular, for two and three spatial dimensions, it is found from the behavior of the third virial coefficient of the model that the deformation parameter q interpolates completely between attractive and repulsive systems, including the free boson and fermion cases. From the results obtained in this work, we conclude that such a model could provide much physical insight into some interacting theories of fermions, and could be useful to further study the particle systems with intermediate statistics.

Thermodynamics of a two-parameter deformed quantum group boson gas

Abstract A two-parameter deformed quantum group boson gas with SU q 1 / q 2 (2) symmetry is discussed and for high temperatures, its thermodynamical properties obtained by means of a SU q 1 / q 2 (2)-invariant bosonic Hamiltonian are investigated in terms of the deformation parameters q 1 and q 2 . The usual boson gas results can be recovered in the limit q 1 = q 2 =1.

Non-extensive entropy of bosonic Fibonacci oscillators

We discuss possible connections between the thermostatistical properties of a gas of the two-parameter deformed bosonic particles called Fibonacci oscillators and the properties of the Tsallis thermostatistics. In this framework, we particularly focus on a comparison of the non-extensive entropy functions expressed by these two generalized theories. We also show that the thermostatistics of the two-parameter deformed bosons can be studied using the formalism of Fibonacci calculus, which generalizes the recently proposed formalism of Lavagno and Narayana Swamy of q-calculus for the one-parameter deformed boson gas. As an application, we briefly summarize some of the recent results on the Bose–Einstein condensation phenomenon for the present two-parameter generalized boson gas.

Bose-Einstein condensation in a gas of the bosonic Newton oscillators

The multi-dimensional q-deformed bosonic Newton oscillator algebra with U(d)-symmetry is considered. The high- and low-temperature thermostatistical properties of a gas of the q-deformed bosonic Newton oscillators are obtained in the thermodynamical limit. It is shown that the Bose–Einstein condensation occurs in such a gas for values of the real deformation parameter q smaller than 1. However, the ordinary boson gas results can be recovered in the limit q = 1.

A TWO-PARAMETER DEFORMED SUSY ALGEBRA FOR SUp/q(n)-COVARIANT (p,q)-DEFORMED FERMIONIC OSCILLATORS

A two-parameter deformed superoscillator system with SUq1/q2(n|m)-covariance is presented and used to construct a two-parameter deformed N=2 SUSY algebra. The Fock space representation of the algebra is discussed and the deformed Hamiltonian for such generalized superoscillators is obtained.We construct a two-parameter deformed SUSY algebra by constructing SUSY generators which are bilinears of n (p,q)-deformed fermions covariant under the quantum group SUp/q(n) and n undeformed bosons. The Fock space representation of the algebra constructed is discussed and the total deformed Hamiltonian for such a system is obtained. Some physical applications of the quantum group covariant two-parameter deformed fermionic oscillator algebra are also considered.

A Two-Parameter Deformed N = 2 SUSY Algebra

A two-parameter deformed N = 2 SUSY algebra is constructed by using the q-deformed bosonic and fermionic Newton oscillator algebras. The Fock space representation of the (q1,q2)-deformed N = 2 SUSY algebra is analyzed. The comparison between the algebra constructed and earlier versions of deformed N = 2 SUSY algebras is also made.

Thermostatistics of bosonic and fermionic Fibonacci oscillators

In this work, we first introduce some new properties concerning the Fibonacci calculus. We then discuss the thermostatistics of gas models of two-parameter deformed oscillators, called bosonic and fermionic Fibonacci oscillators, in the thermodynamical limit. In this framework, we analyze the behavior of two-parameter deformed mean occupation numbers describing the Fibonacci-type bosonic and fermionic intermediate-statistics particles. A virial expansion of the equation of state for the bosonic Fibonacci oscillators’ gas model is obtained in both two and three dimensions, and the first five virial coefficients are derived in terms of the real independent deformation parameters p and q. The effect of bosonic and fermionic p, q-deformation on the thermostatistical properties of Fibonacci-type p, q-boson and p, q-fermion gas models are also discussed. The results obtained in this work can be useful for investigating some exotic quasiparticle states encountered in condensed matter systems.

General thermostatistical properties of a q-deformed fermion gas in two dimensions

Starting with a deformed fermionic grand partition function, we study the high and low temperature thermostatistical properties of a special q-deformed fermion gas in two spatial dimensions. Many of the deformed thermostatistical functions such as the specific heat and the entropy are derived in terms of the real deformation parameter q for the range q < 1. For high temperatures, we specifically focus on the behavior of both the entropy function and the deformed virial coefficients in the equation of state for the q-fermion gas in two dimensions. Possible physical applications of the present q-fermion gas are briefly discussed.

q-Deformed Tamm–Dancoff oscillators: Representation, fermionic extension and physical application

In this paper, the q-deformed bosonic Tamm–Dancoff oscillator algebra is considered. First, the quantum algebraic and representative properties of these deformed bosons are analyzed in detail. The representations of the q-fermion algebra of Tamm–Dancoff type are also studied. Second, the high-temperature thermostatistical properties of a gas of Tamm–Dancoff type q-fermions are investigated. The fermionic distribution function and the other important thermodynamic functions such as the entropy and the specific heat are derived in terms of the real deformation parameter q. Finally, the time evaluation of a two-level atom in a Tamm–Dancoff oscillator trap interacting with a single-mode traveling light field is concisely discussed.