q-deformed Fermions

This is a study of $q$-Fermions arising from a q-deformed algebra of harmonic oscillators. Two distinct algebras will be investigated. Employing the first algebra, the Fock states are constructed for the generalized Fermions obeying Pauli exclusion principle. The distribution function and other thermodynamic properties such as the internal energy and entropy are derived. Another generalization of fermions from a different q-deformed algebra is investigated which deals with q-fermions not obeying the exclusion principle. Fock states are constructed for this system. The basic numbers appropriate for this system are determined as a direct consequence of the algebra. We also establish the Jackson Derivative, which is required for the q-calculus needed to describe these generalized Fermions.Comment: 10 pages, Revtex forma

q-deformed fermion oscillators, zero-point energy and inclusion-exclusion principle

The theory of Fermion oscillators has two essential ingredients: zero-point energy and Pauli exclusion principle. We devlop the theory of the statistical mechanics of generalized q-deformed Fermion oscillator algebra with inclusion principle (i.e., without the exclusion principle), which corresponds to ordinary fermions with Pauli exclusion principle in the classical limit $q \to 1$. Some of the remarkable properties of this theory play a crucial role in the understanding of the q-deformed Fermions. We show that if we insist on the weak exclusion principle, then the theory has the expected low temperature limit as well as the correct classical q-limit.Comment: 10 pages, Latex, submitted to Physical Review

Temporal Decomposition Studies of GRB Lightcurves

Gamma-ray bursts (GRB) are extremely energetic events and produce highly diverse light curves. Light curves are believed to be resulting from internal shocks reflecting the activities of the GRB central engine. Hence their temporal studies can potentially lead to the understanding of the GRB central engine and its evolution. The light curve variability time scale is an interesting parameter which most models attribute to a physical origin e.g., central engine activity, clumpy circumburst medium, or relativistic turbulence. We develop a statistical method to estimate the GRB minimum variability time scale (MVT) for long and short GRBs detected by GBM. We find that the MVT of short bursts is distinctly shorter than that for long GRBs supprting the possibility of a more compact central engine of the former. We find that MVT estimated by this method is consistent with the shortest rise time of the fitted pulses. Hence we use the fitted pulse rise times to study the evolution of burst variability time scale. Variability time is in turn related to the minimum bulk Lorentz factor. Using this we relate the GRB spectral evolution to the evolution of the variability time scale. %Gamma-ray burst (GRB) light curves are believed to result from internal shocks reflecting the activities of the GRB central engine. %Hence their temporal deconvolution studies can potentially lead to the understanding of the evolution of the minimum variability %time scales which in turn is related to the minimum bulk Lorentz factor. We relate the GRB spectral evolution to the evolution of the %minimum variability time scale.Comment: 5 pages 6 figures. Presented at GRB2012 at Marbella, Spai

Deformed Heisenberg algebra: origin of q-calculus

The intimate connection between q-deformed Heisenberg uncertainty relation and the Jackson derivative based on q-basic numbers has been noted in the literature. The purpose of this work is to establish this connection in a clear and self-consistent formulation and to show explicitly how the Jackson derivative arises naturally. We utilize a holomorphic representation to arrive at the correct algebra to describe q-deformed bosons. We investigate the algebra of q-fermions and point out how different it is from the theory of q-bosons. We show that the holomorphic representation for q-fermions is indeed feasible in the framework of the theory of generalized fermions. We also examine several different q-algebras in the context of the modified Heisenberg equation of motion.Comment: 11 page