10,396 research outputs found
q-deformed Fermions
This is a study of -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
A Meaningful MD5 Hash Collision Attack
It is now proved by Wang et al., that MD5 hash is no more secure, after they proposed an attack that would generate two different messages that gives the same MD5 sum. Many conditions need to be satisfied to attain this collision. Vlastimil Klima then proposed a more efficient and faster technique to implement this attack. We use these techniques to first create a collision attack and then use these collisions to implement meaningful collisions by creating two different packages that give identical MD5 hash, but when extracted, each gives out different files with contents specified by the atacker
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 . 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
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