Ali Serdar Arikan

Inhomogeneous Quantum Invariance Group of Multi-Dimensional Multi-parameter Deformed Boson Algebra

We investigate the inhomogeneous invariance quantum group of the d-dimensional d-parameter deformed boson algebra. It is found that the homogeneous part of this quantum group is given by the d-parameter deformed general linear group. We construct the R-matrix which collects all information about the non-commuting structure of the quantum group for the two-dimensional case.

THE INHOMOGENEOUS INVARIANCE QUANTUM GROUP OF Q-DEFORMED BOSON ALGEBRA WITH CONTINUOUS PARAMETERS

We present a q-deformed boson algebra using continuous momentum parameters and investigate its inhomogeneous invariance quantum group.

The inhomogeneous quantum invariance group of the multi-dimensional q-deformed boson algebra

In this study we introduce a multi-dimensional q-deformed boson algebra and calculate its inhomogeneous invariance quantum group.

The multi-dimensional q-deformed bosonic Newton oscillator and its inhomogeneous quantum invariance group

AbstractWe obtain the inhomogeneous invariance quantum group for the multi-dimensional q-deformed bosonic Newton oscillator algebra. The homogenous part of this quantum group is given by the multiparameter quantum group

Effective approach for taking into account interactions of quasiparticles from the low-temperature behavior of a deformed fermion-gas model

GL_{X;q_{ij} }

High temperature behavior of a two-parameter deformed quantum group fermion gas

of Schirrmacher where qij’s take some special values. We find the R-matrix which gives the non-commuting structure of the quantum group for the two dimensional case.

High temperature thermostatistics of fermionic Fibonacci oscillators with intermediate statistics

We investigate the inhomogeneous invariance group of the q-deformed boson algebra. We find the R-matrix which gives the noncommuting structure of the quantum group with RM1M2 = M2M1R relation.

The Inhomogeneous Quantum Invariance Group of The Two Parameter Deformed Boson Algebra

A deformed fermion gas model aimed at taking into account thermal and electronic properties of quasiparticle systems is devised. The model is constructed by the fermionic Fibonacci oscillators whose spectrum is given by a generalized Fibonacci sequence. We first introduce some new properties concerning the Fibonacci calculus. We then investigate the low-temperature thermostatistical properties of the model, and derive many of the deformed thermostatistical functions such as the chemical potential and the entropy in terms of the model deformation parameters p and q. We specifically focus on the p,q-deformed Sommerfeld parameter for the heat capacity of the model, and its behavior is compared with those of both the free-electron Fermi theory and the experimental data for some materials. The results obtained in this study reveal that the present deformed fermion model leads to an effective approach accounting for interaction and compositeness of quasiparticles, which have remarkable implications in many technological applications such as in nanomaterials.