964 research outputs found
Noncommutative Quantum Hall Effect and Aharonov-Bohm Effect
We study a system of electrons moving on a noncommutative plane in the
presence of an external magnetic field which is perpendicular to this plane.
For generality we assume that the coordinates and the momenta are both
noncommutative. We make a transformation from the noncommutative coordinates to
a set of commuting coordinates and then we write the Hamiltonian for this
system. The energy spectrum and the expectation value of the current can then
be calculated and the Hall conductivity can be extracted. We use the same
method to calculate the phase shift for the Aharonov-Bohm effect. Precession
measurements could allow strong upper limits to be imposed on the
noncommutativity coordinate and momentum parameters and .Comment: 9 pages, RevTeX4, references added, small changes in the tex
Asymptotic Stability for a Class of Metriplectic Systems
Using the framework of metriplectic systems on we will describe a
constructive geometric method to add a dissipation term to a Hamilton-Poisson
system such that any solution starting in a neighborhood of a nonlinear stable
equilibrium converges towards a certain invariant set. The dissipation term
depends only on the Hamiltonian function and the Casimir functions
The decay constants of pseudoscalar mesons in a relativistic quark model
The decay constants of pseudoscalar mesons are calculated in a relativistic
quark model which assumes that mesons are made of a valence quark antiquark
pair and of an effective vacuum like component. The results are given in terms
of quark masses and of some free parameters entering the expression of the
internal wave functions of the mesons. By using the pion and kaon decay
constants to fix the parameters of the
model one gets for the light quark masses
and the heavy quark masses in the
range: . In the case of
light neutral mesons one obtains with the same set of parameters
. The
values are in agreement with the experimental data and other theoretical
results.Comment: 11 pages, LaTe
Quantum mechanics on non commutative spaces and squeezed states: a functional approach
We review here the quantum mechanics of some noncommutative theories in which
no state saturates simultaneously all the non trivial Heisenberg uncertainty
relations. We show how the difference of structure between the Poisson brackets
and the commutators in these theories generically leads to a harmonic
oscillator whose positions and momenta mean values are not strictly equal to
the ones predicted by classical mechanics.
This raises the question of the nature of quasi classical states in these
models. We propose an extension based on a variational principle. The action
considered is the sum of the absolute values of the expressions associated to
the non trivial Heisenberg uncertainty relations. We first verify that our
proposal works in the usual theory i.e we recover the known Gaussian functions.
Besides them, we find other states which can be expressed as products of
Gaussians with specific hyper geometrics.
We illustrate our construction in two models defined on a four dimensional
phase space: a model endowed with a minimal length uncertainty and the non
commutative plane. Our proposal leads to second order partial differential
equations. We find analytical solutions in specific cases. We briefly discuss
how our proposal may be applied to the fuzzy sphere and analyze its
shortcomings.Comment: 15 pages revtex. The title has been modified,the paper shortened and
misprints have been corrected. Version to appear in JHE
Financial news analysis using a semantic web approach
In this paper we present StockWatcher, an OWL-based web application that enables the extraction of relevant news items from RSS feeds concerning the NASDAQ-100 listed companies. The application's goal is to present a customized, aggregated view of the news categorized by different topics. We distinguish between four relevant news categories: i) news regarding the company itself, ii) news regarding direct competitors of the company, iii) news regarding important people of the company, and iv) news regarding the industry in which the company is active. At the same time, the system presented in this chapter is able to rate these news items based on their relevance. We identify three possible effects that a news message can have on the company, and thus on the stock price of that company: i) positive, ii) negative, and iii) neutral. Currently, StockWatcher provides support for the NASDAQ-100 companies. The selection of the relevant news items is based on a customizable user portfolio that may consist of one or more of these companies
One-loop renormalization of general noncommutative Yang-Mills field model coupled to scalar and spinor fields
We study the theory of noncommutative U(N) Yang-Mills field interacting with
scalar and spinor fields in the fundamental and the adjoint representations. We
include in the action both the terms describing interaction between the gauge
and the matter fields and the terms which describe interaction among the matter
fields only. Some of these interaction terms have not been considered
previously in the context of noncommutative field theory. We find all
counterterms for the theory to be finite in the one-loop approximation. It is
shown that these counterterms allow to absorb all the divergencies by
renormalization of the fields and the coupling constants, so the theory turns
out to be multiplicatively renormalizable. In case of 1PI gauge field functions
the result may easily be generalized on an arbitrary number of the matter
fields. To generalize the results for the other 1PI functions it is necessary
for the matter coupling constants to be adapted in the proper way. In some
simple cases this generalization for a part of these 1PI functions is
considered.Comment: 1+26 pages, figures using axodraw, clarifications adde
Cornwall-Jackiw-Tomboulis effective potential for canonical noncommutative field theories
We apply the Cornwall-Jackiw-Tomboulis (CJT) formalism to the scalar theory in canonical-noncommutative spacetime. We construct the CJT
effective potential and the gap equation for general values of the
noncommutative parameter . We observe that under the
hypothesis of translational invariance, which is assumed in the effective
potential construction, differently from the commutative case
(), the renormalizability of the gap equation is
incompatible with the renormalizability of the effective potential. We argue
that our result, is consistent with previous studies suggesting that a uniform
ordered phase would be inconsistent with the infrared structure of canonical
noncommutative theories.Comment: 15 pages, LaTe
Effect of Minimal lengths on Electron Magnetism
We study the magnetic properties of electron in a constant magnetic field and
confined by a isotropic two dimensional harmonic oscillator on a space where
the coordinates and momenta operators obey generalized commutation relations
leading to the appearance of a minimal length. Using the momentum space
representation we determine exactly the energy eigenvalues and eigenfunctions.
We prove that the usual degeneracy of Landau levels is removed by the presence
of the minimal length in the limits of weak and strong magnetic field.The
thermodynamical properties of the system, at high temperature, are also
investigated showing a new magnetic behavior in terms of the minimal length.Comment: 14 pages, 1 figur
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