19,944 research outputs found
The scalar complex potential and the Aharonov-Bohm effect
The Aharonov-Bohm effect is traditionally attributed to the effect of the
electromagnetic 4-potential , even in regions where both the electric field
and the magnetic field are zero. The AB effect
reveals that multiple-valued functions play a crucial role in the description
of an electromagnetic field. We argue that the quantity measured by AB
experiments is a difference in values of a multiple-valued complex function,
which we call a complex potential or {pre-potential. We show that any
electromagnetic field can be described by this pre-potential, and give an
explicit expression for the electromagnetic field tensor through this
potential. The pre-potential is a modification of the two scalar potential
functions.Comment: 10 pages 2 figure
Fixed subgroups are compressed in surface groups
For a compact surface (orientable or not, and with boundary or not)
we show that the fixed subgroup, , of any family of
endomorphisms of is compressed in i.e.,
for
any subgroup . On the way, we
give a partial positive solution to the inertia conjecture, both for free and
for surface groups. We also investigate direct products, , of finitely many
free and surface groups, and give a characterization of when satisfies that
for
every
Reactions at Polymer Interfaces: Transitions from Chemical to Diffusion-Control and Mixed Order Kinetics
We study reactions between end-functionalized chains at a polymer-polymer
interface. For small chemical reactivities (the typical case) the number of
diblocks formed, , obeys 2nd order chemically controlled kinetics, , until interfacial saturation. For high reactivities (e.g. radicals) a
transition occurs at short times to 2nd order diffusion-controlled kinetics,
with for unentangled chains while and
regimes occur for entangled chains. Long time kinetics are 1st order and
controlled by diffusion of the more dilute species to the interface: for unentangled cases, while and regimes
arise for entangled systems. The final 1st order regime is governed by center
of gravity diffusion, .Comment: 11 pages, 3 figures, uses poliface.sty, minor changes, to appear in
Europhysics Letter
Occurrence of normal and anomalous diffusion in polygonal billiard channels
From extensive numerical simulations, we find that periodic polygonal
billiard channels with angles which are irrational multiples of pi generically
exhibit normal diffusion (linear growth of the mean squared displacement) when
they have a finite horizon, i.e. when no particle can travel arbitrarily far
without colliding. For the infinite horizon case we present numerical tests
showing that the mean squared displacement instead grows asymptotically as t
log t. When the unit cell contains accessible parallel scatterers, however, we
always find anomalous super-diffusion, i.e. power-law growth with an exponent
larger than 1. This behavior cannot be accounted for quantitatively by a simple
continuous-time random walk model. Instead, we argue that anomalous diffusion
correlates with the existence of families of propagating periodic orbits.
Finally we show that when a configuration with parallel scatterers is
approached there is a crossover from normal to anomalous diffusion, with the
diffusion coefficient exhibiting a power-law divergence.Comment: 9 pages, 15 figures. Revised after referee reports: redrawn figures,
additional comments. Some higher quality figures available at
http://www.fis.unam.mx/~dsander
On wormholes with arbitrarily small quantities of exotic matter
Recently several models of traversable wormholes have been proposed which
require only arbitrarily small amounts of negative energy to hold them open
against self-collapse. If the exotic matter is assumed to be provided by
quantum fields, then quantum inequalities can be used to place constraints on
the negative energy densities required. In this paper, we introduce an
alternative method for obtaining constraints on wormhole geometries, using a
recently derived quantum inequality bound on the null-contracted stress-energy
averaged over a timelike worldline. The bound allows us to perform a simplified
analysis of general wormhole models, not just those with small quantities of
exotic matter. We then use it to study, in particular, the models of Visser,
Kar, and Dadhich (VKD) and the models of Kuhfittig. The VKD models are
constrained to be either submicroscopic or to have a large discrepancy between
throat size and curvature radius. A recent model of Kuhfittig is shown to be
non-traversable. This is due to the fact that the throat of his wormhole flares
outward so slowly that light rays and particles, starting from outside the
throat, require an infinite lapse of affine parameter to reach the throat.Comment: 30 pages, 2 figure
Anomalous Hall Effect in Ferromagnetic Semiconductors in the Hopping Transport Regime
We present a theory of the Anomalous Hall Effect (AHE) in ferromagnetic
(Ga,Mn)As in the regime when conduction is due to phonon-assisted hopping of
holes between localized states in the impurity band. We show that the
microscopic origin of the anomalous Hall conductivity in this system can be
attributed to a phase that a hole gains when hopping around closed-loop paths
in the presence of spin-orbit interactions and background magnetization of the
localized Mn moments. Mapping the problem to a random resistor network, we
derive an analytic expression for the macroscopic anomalous Hall conductivity
. We show that is proportional to the
first derivative of the density of states and thus can be
expected to change sign as a function of impurity band filling. We also show
that depends on temperature as the longitudinal conductivity
within logarithmic accuracy.Comment: 4 pages, 1 eps figure, final versio
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