65 research outputs found
Tensor Coordinates in Noncommutative Mechanics
A consistent classical mechanics formulation is presented in such a way that,
under quantization, it gives a noncommutative quantum theory with interesting
new features. The Dirac formalism for constrained Hamiltonian systems is
strongly used, and the object of noncommutativity plays
a fundamental rule as an independent quantity. The presented classical theory,
as its quantum counterpart, is naturally invariant under the rotation group
.Comment: 12 pages, Late
Noncommutative Complex Scalar Field and Casimir Effect
A noncommutative complex scalar field, satisfying the deformed canonical
commutation relations proposed by Carmona et al. [27]-[31], is constructed.
Using these noncommutative deformed canonical commutation relations, a model
describing the dynamics of the noncommutative complex scalar field is proposed.
The noncommutative field equations are solved, and the vacuum energy is
calculated to the second order in the parameter of noncommutativity. As an
application to this model, the Casimir effect, due to the zero point
fluctuations of the noncommutative complex scalar field, is considered. It
turns out that in spite of its smallness, the noncommutativity gives rise to a
repulsive force at the microscopic level, leading to a modifed Casimr potential
with a minimum at the point amin= racine(5/84){\pi}{\theta}.Comment: Revtex style, 28 page
Formulation, Interpretation and Application of non-Commutative Quantum Mechanics
In analogy with conventional quantum mechanics, non-commutative quantum
mechanics is formulated as a quantum system on the Hilbert space of
Hilbert-Schmidt operators acting on non-commutative configuration space. It is
argued that the standard quantum mechanical interpretation based on Positive
Operator Valued Measures, provides a sufficient framework for the consistent
interpretation of this quantum system. The implications of this formalism for
rotational and time reversal symmetry are discussed. The formalism is applied
to the free particle and harmonic oscillator in two dimensions and the physical
signatures of non commutativity are identified.Comment: 11 page
The ecological diversity of vegetation within Urban Parks in the Dabrowski Basin (southern Poland)
The aim of this work is to present the diversity of flora in terms of ecological requirements. The research was
conducted in the area of two urban parks in the area of two cities in southern Poland: Bedzin and Czeladz. These parks were
established in different historical periods, and were planned (and are managed) differently. The results of the investigation
have shown that the occurrence of 192 vascular species has been observed in the Gora Zamkowa (Castle Hill) Park, while in
the Grabek park, 334 such species are known to exist. Such disparity is the result of the occurrence of micro-habitats and of
the differences between the ways the two parks are managed. It is also due to these parks’ different functions. In the first case,
the park area is protected by law. In the latter case, human activity has created a new ecological niche for organisms with a
high degree of ecological tolerance. Based on the ecological values, the following groups of plants were distinguished: saxifrages
grasslands, xerothermic grasslands, beech forests, alder forests and artificial planted trees. Analysis has shown that urban
parks are potential places for growth various type of vegetation and also for increasing biodiversity, and can constitute
particularly important hotspots for biodiversity in the cityscape, even if their primary role is recreational. As the study shows,
the environment of a highly urbanized and industrialized region can also have a positive influence on ecological and floristic
diversity
Numerical study of the coupled time-dependent Gross-Pitaevskii equation: Application to Bose-Einstein condensation
We present a numerical study of the coupled time-dependent Gross-Pitaevskii
equation, which describes the Bose-Einstein condensate of several types of
trapped bosons at ultralow temperature with both attractive and repulsive
interatomic interactions. The same approach is used to study both stationary
and time-evolution problems. We consider up to four types of atoms in the study
of stationary problems. We consider the time-evolution problems where the
frequencies of the traps or the atomic scattering lengths are suddenly changed
in a stable preformed condensate. We also study the effect of periodically
varying these frequencies or scattering lengths on a preformed condensate.
These changes introduce oscillations in the condensate which are studied in
detail. Good convergence is obtained in all cases studied.Comment: 9 pages, 10 figures, accepted in Physical Review
Photon Physics in Heavy Ion Collisions at the LHC
Various pion and photon production mechanisms in high-energy nuclear
collisions at RHIC and LHC are discussed. Comparison with RHIC data is done
whenever possible. The prospect of using electromagnetic probes to characterize
quark-gluon plasma formation is assessed.Comment: Writeup of the working group "Photon Physics" for the CERN Yellow
Report on "Hard Probes in Heavy Ion Collisions at the LHC", 134 pages. One
figure added in chapter 5 (comparison with PHENIX data). Some figures and
correponding text corrected in chapter 6 (off-chemical equilibrium thermal
photon rates). Some figures modified in chapter 7 (off-chemical equilibrium
photon rates) and comparison with PHENIX data adde
Magnetic fields in noncommutative quantum mechanics
We discuss various descriptions of a quantum particle on noncommutative space
in a (possibly non-constant) magnetic field. We have tried to present the basic
facts in a unified and synthetic manner, and to clarify the relationship
between various approaches and results that are scattered in the literature.Comment: Dedicated to the memory of Julius Wess. Work presented by F. Gieres
at the conference `Non-commutative Geometry and Physics' (Orsay, April 2007
Signatures of Large Extra Dimensions
String theory suggests modifications of our spacetime such as extra
dimensions and the existence of a mininal length scale. In models with
addidional dimensions, the Planck scale can be lowered to values accessible by
future colliders. Effective theories which extend beyond the standart-model by
including extra dimensions and a minimal length allow computation of
observables and can be used to make testable predictions. Expected effects that
arise within these models are the production of gravitons and black holes.
Furthermore, the Planck-length is a lower bound to the possible resolution of
spacetime which might be reached soon.Comment: 8 pages, no figures, Talk presented at the NATO Advanced Study
Institute: Structure and Dynamics of Elementary Matter, Kemer, Turkey, 22 Sep
- 2 Oct 2003. Proceedings to be published by Kluwer Academic publisher
Signatures in the Planck Regime
String theory suggests the existence of a minimum length scale. An exciting
quantum mechanical implication of this feature is a modification of the
uncertainty principle. In contrast to the conventional approach, this
generalised uncertainty principle does not allow to resolve space time
distances below the Planck length. In models with extra dimensions, which are
also motivated by string theory, the Planck scale can be lowered to values
accessible by ultra high energetic cosmic rays (UHECRs) and by future
colliders, i.e. 1 TeV. It is demonstrated that in this novel
scenario, short distance physics below is completely cloaked by the
uncertainty principle. Therefore, Planckian effects could be the final physics
discovery at future colliders and in UHECRs. As an application, we predict the
modifications to the cross-sections.Comment: 14 pages, 4 figures, typos corrected, references adde
Dynamical Renormalization Group Approach to Quantum Kinetics in Scalar and Gauge Theories
We derive quantum kinetic equations from a quantum field theory implementing
a diagrammatic perturbative expansion improved by a resummation via the
dynamical renormalization group. The method begins by obtaining the equation of
motion of the distribution function in perturbation theory. The solution of
this equation of motion reveals secular terms that grow in time, the dynamical
renormalization group resums these secular terms in real time and leads
directly to the quantum kinetic equation. We used this method to study the
relaxation in a cool gas of pions and sigma mesons in the O(4) chiral linear
sigma model. We obtain in relaxation time approximation the pion and sigma
meson relaxation rates. We also find that in large momentum limit emission and
absorption of massless pions result in threshold infrared divergence in sigma
meson relaxation rate and lead to a crossover behavior in relaxation. We then
study the relaxation of charged quasiparticles in scalar electrodynamics
(SQED). While longitudinal, Debye screened photons lead to purely exponential
relaxation, transverse photons, only dynamically screened by Landau damping
lead to anomalous relaxation, thus leading to a crossover between two different
relaxational regimes. We emphasize that infrared divergent damping rates are
indicative of non-exponential relaxation and the dynamical renormalization
group reveals the correct relaxation directly in real time. Finally we also
show that this method provides a natural framework to interpret and resolve the
issue of pinch singularities out of equilibrium and establish a direct
correspondence between pinch singularities and secular terms. We argue that
this method is particularly well suited to study quantum kinetics and transport
in gauge theories.Comment: RevTeX, 40 pages, 4 eps figures, published versio
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