25,299 research outputs found
Non-unitary representations of the SU(2) algebra in the Dirac equation with a Coulomb potential
A novel realization of the classical SU(2) algebra is introduced for the
Dirac relativistic hydrogen atom defining a set of operators that, besides,
allow the factorization of the problem. An extra phase is needed as a new
variable in order to define the algebra. We take advantage of the operators to
solve the Dirac equation using algebraic methods. To acomplish this, a similar
path to the one used in the angular momentum case is employed; hence, the
radial eigenfuntions calculated comprise non unitary representations of the
algebra. One of the interesting properties of such non unitary representations
is that they are not labeled by integer nor by half-integer numbers as happens
in the usual angular momentum representation.Comment: 20 pages 1 eps figure in a single zipped file, submitted to J. Math.
Phy
Capturing pattern bi-stability dynamics in delay-coupled swarms
Swarms of large numbers of agents appear in many biological and engineering
fields. Dynamic bi-stability of co-existing spatio-temporal patterns has been
observed in many models of large population swarms. However, many reduced
models for analysis, such as mean-field (MF), do not capture the bifurcation
structure of bi-stable behavior. Here, we develop a new model for the dynamics
of a large population swarm with delayed coupling. The additional physics
predicts how individual particle dynamics affects the motion of the entire
swarm. Specifically, (1) we correct the center of mass propulsion physics
accounting for the particles velocity distribution; (2) we show that the model
we develop is able to capture the pattern bi-stability displayed by the full
swarm model.Comment: 6 pages 4 figure
An algebraic SU(1,1) solution for the relativistic hydrogen atom
The bound eigenfunctions and spectrum of a Dirac hydrogen atom are found
taking advantage of the Lie algebra in which the radial part of the
problem can be expressed. For defining the algebra we need to add to the
description an additional angular variable playing essentially the role of a
phase. The operators spanning the algebra are used for defining ladder
operators for the radial eigenfunctions of the relativistic hydrogen atom and
for evaluating its energy spectrum. The status of the Johnson-Lippman operator
in this algebra is also investigated.Comment: to appear in Physics Letters A (2005). We corrected a misprint in
page 7, in the paragraph baggining with "With the value of ..." the ground
state should be |\lambda, \lambda>, not |\lambda, \lambda+1
Increase of the Energy Necessary to Probe Ultraviolet Theories Due to the Presence of a Strong Magnetic Field
We use the gauge gravity correspondence to study the renormalization group
flow of a double trace fermionic operator in a quark-gluon plasma subject to
the influence of a strong magnetic field and compare it with the results for
the case at zero temperature and no magnetic field, where the flow between two
fixed points is observed. Our results show that the energy necessary to access
the physics of the ultraviolet theory increases with the intensity of the
magnetic field under which the processes happen. We provide arguments to
support that this increase is scheme independent, and to exhibit further
evidence we do a very simple calculation showing that the dimensional reduction
expected in the gauge theory in this scenario is effective up to an energy
scale that grows with the strength of such a background field. We also show
that independently of the renormalization scheme, the coupling of the double
trace operators in the ultraviolet fixed point increases with the intensity of
the background field. These effects combined can change both, the processes
that are expected to be involved in a collision experiment at a given energy
and the azimuthal anisotropy of the measurements resulting of them.Comment: 23 pages, 10 figures. Added section about renormalization scheme
independenc
Noise, Bifurcations, and Modeling of Interacting Particle Systems
We consider the stochastic patterns of a system of communicating, or coupled,
self-propelled particles in the presence of noise and communication time delay.
For sufficiently large environmental noise, there exists a transition between a
translating state and a rotating state with stationary center of mass. Time
delayed communication creates a bifurcation pattern dependent on the coupling
amplitude between particles. Using a mean field model in the large number
limit, we show how the complete bifurcation unfolds in the presence of
communication delay and coupling amplitude. Relative to the center of mass, the
patterns can then be described as transitions between translation, rotation
about a stationary point, or a rotating swarm, where the center of mass
undergoes a Hopf bifurcation from steady state to a limit cycle. Examples of
some of the stochastic patterns will be given for large numbers of particles
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