1,113 research outputs found
Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, Symbols, and Character Localization
In this paper we employ a novel technique combining the Euler Maclaurin
formula with the saddle point approximation method to obtain the asymptotic
behavior (in the limit of large representation index ) of generic Wigner
matrix elements . We use this result to derive asymptotic
formulae for the character of an SU(2) group element and for
Wigner's symbol. Surprisingly, given that we perform five successive
layers of approximations, the asymptotic formula we obtain for is
in fact exact. This result provides a non trivial example of a
Duistermaat-Heckman like localization property for discrete sums.Comment: 36 pages, 3 figure
Correlation studies of open and closed states fluctuations in an ion channel: Analysis of ion current through a large conductance locust potassium channel
Ion current fluctuations occurring within open and closed states of large
conductance locust potassium channel (BK channel) were investigated for the
existence of correlation. Both time series, extracted from the ion current
signal, were studied by the autocorrelation function (AFA) and the detrended
fluctuation analysis (DFA) methods. The persistent character of the short- and
middle-range correlations of time series is shown by the slow decay of the
autocorrelation function. The DFA exponent is significantly larger
than 0.5. The existence of strongly-persistent long-range correlations was
detected only for closed-states fluctuations, with . The
long-range correlation of the BK channel action is therefore determined by the
character of closed states. The main outcome of this study is that the memory
effect is present not only between successive conducting states of the channel
but also independently within the open and closed states themselves. As the ion
current fluctuations give information about the dynamics of the channel
protein, our results point to the correlated character of the protein movement
regardless whether the channel is in its open or closed state.Comment: 12 pages, 5 figures; to be published in Phys. Rev.
Chiral-symmetry restoration in the linear sigma model at nonzero temperature and baryon density
We study the chiral phase transition in the linear sigma model with 2 quark
flavors and colors. One-loop calculations predict a first-order phase
transition at both and . We also discuss the phase diagram
and make a comparison with a thermal parametrization of existing heavy-ion
experimental data.Comment: 12 pages, 6 ps-figures, LaTe
Oscillatory wave fronts in chains of coupled nonlinear oscillators
Wave front pinning and propagation in damped chains of coupled oscillators
are studied. There are two important thresholds for an applied constant stress
: for (dynamic Peierls stress), wave fronts fail to propagate,
for stable static and moving wave fronts coexist, and
for (static Peierls stress) there are only stable moving wave
fronts. For piecewise linear models, extending an exact method of Atkinson and
Cabrera's to chains with damped dynamics corroborates this description. For
smooth nonlinearities, an approximate analytical description is found by means
of the active point theory. Generically for small or zero damping, stable wave
front profiles are non-monotone and become wavy (oscillatory) in one of their
tails.Comment: 18 pages, 21 figures, 2 column revtex. To appear in Phys. Rev.
Influence of Impact Parameter on Thermal Description of Relativistic Heavy Ion Collisions at GSI/SIS
Attention is drawn to the role played by the size of the system in the
thermodynamic analysis of particle yields in relativistic heavy ion collisions
at SIS energies. This manifests itself in the non-linear dependence of K+ and
K- yields in collisions at 1 -- 2 A.GeV on the number of participants. It
is shown that this dependence can be quantitatively well described in terms of
a thermal model with a canonical strangeness conservation. The measured
particle multiplicity ratios (pi+/p, pi-/pi+, d/p, K+/pi+ and K+/K- but not
eta/pi0) in central Au-Au and Ni-Ni collisions at 0.8 -- 2.0 A.GeV are also
explained in the context of a thermal model with a common freeze-out
temperature and chemical potential. Including the concept of collective flow a
consistent picture of particle energy distributions is derived with the flow
velocity being strongly impact-parameter dependent.Comment: revtex, 20 figure
Hexagonal dielectric resonators and microcrystal lasers
We study long-lived resonances (lowest-loss modes) in hexagonally shaped
dielectric resonators in order to gain insight into the physics of a class of
microcrystal lasers. Numerical results on resonance positions and lifetimes,
near-field intensity patterns, far-field emission patterns, and effects of
rounding of corners are presented. Most features are explained by a
semiclassical approximation based on pseudointegrable ray dynamics and boundary
waves. The semiclassical model is also relevant for other microlasers of
polygonal geometry.Comment: 12 pages, 17 figures (3 with reduced quality
Knots, Braids and BPS States in M-Theory
In previous work we considered M-theory five branes wrapped on elliptic
Calabi-Yau threefold near the smooth part of the discriminant curve. In this
paper, we extend that work to compute the light states on the worldvolume of
five-branes wrapped on fibers near certain singular loci of the discriminant.
We regulate the singular behavior near these loci by deforming the discriminant
curve and expressing the singularity in terms of knots and their associated
braids. There braids allow us to compute the appropriate string junction
lattice for the singularity and,hence to determine the spectrum of light BPS
states. We find that these techniques are valid near singular points with N=2
supersymmetry.Comment: 38 page
Sublocalization, superlocalization, and violation of standard single parameter scaling in the Anderson model
We discuss the localization behavior of localized electronic wave functions
in the one- and two-dimensional tight-binding Anderson model with diagonal
disorder. We find that the distributions of the local wave function amplitudes
at fixed distances from the localization center are well approximated by
log-normal fits which become exact at large distances. These fits are
consistent with the standard single parameter scaling theory for the Anderson
model in 1d, but they suggest that a second parameter is required to describe
the scaling behavior of the amplitude fluctuations in 2d. From the log-normal
distributions we calculate analytically the decay of the mean wave functions.
For short distances from the localization center we find stretched exponential
localization ("sublocalization") in both, 1d and 2d. In 1d, for large
distances, the mean wave functions depend on the number of configurations N
used in the averaging procedure and decay faster that exponentially
("superlocalization") converging to simple exponential behavior only in the
asymptotic limit. In 2d, in contrast, the localization length increases
logarithmically with the distance from the localization center and
sublocalization occurs also in the second regime. The N-dependence of the mean
wave functions is weak. The analytical result agrees remarkably well with the
numerical calculations.Comment: 12 pages with 9 figures and 1 tabl
Relativistic treatment of harmonics from impurity systems in quantum wires
Within a one particle approximation of the Dirac equation we investigate a
defect system in a quantum wire. We demonstrate that by minimally coupling a
laser field of frequency omega to such an impurity system, one may generate
harmonics of multiples of the driving frequency. In a multiple defect system
one may employ the distance between the defects in order to tune the cut-off
frequency.Comment: 9 pages Latex, 8 eps figures, section added, numerics improve
Covariance of Antiproton Yield and Source Size in Nuclear Collisions
We confront for the first time the widely-held belief that combined
event-by-event information from quark gluon plasma signals can reduce the
ambiguity of the individual signals. We illustrate specifically how the
measured antiproton yield combined with the information from pion-pion HBT
correlations can be used to identify novel event classes.Comment: 8 pages, 5 figures, improved title, references and readability;
results unchange
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