4,036 research outputs found
Heun Functions and the energy spectrum of a charged particle on a sphere under magnetic field and Coulomb force
We study the competitive action of magnetic field, Coulomb repulsion and
space curvature on the motion of a charged particle. The three types of
interaction are characterized by three basic lengths: l_{B} the magnetic
length, l_{0} the Bohr radius and R the radius of the sphere. The energy
spectrum of the particle is found by solving a Schr\"odinger equation of the
Heun type, using the technique of continued fractions. It displays a rich set
of functioning regimes where ratios \frac{R}{l_{B}} and \frac{R}{l_{0}} take
definite values.Comment: 12 pages, 5 figures, accepted to JOPA, november 200
Unitarized pion-nucleon scattering within Heavy Baryon Chiral Perturbation Theory
By means of the Inverse Amplitude Method we unitarize the elastic
pion-nucleon scattering amplitudes obtained from Heavy Baryon Chiral
Perturbation Theory to O(q^3). Within this approach we can enlarge their
applicability range and generate the Delta(1232) resonance. We can find a
reasonable description of the pion nucleon phase shifts with (q^2) parameters
in agreement with the resonance saturation hypothesis. However, the
uncertainties in the analysis of the low energy data as well as the large
number of chiral parameters, which can have strong correlations, allow us to
obtain very good fits with rather different sets of chiral constants.Comment: Shortened version to appear in Phys. Rev. D. Brief Report
Chiral Anomaly and
Measurement of the process has revealed a possible conflict
with what should be a solid prediction generated by the chiral anomaly. We show
that inclusion of appropirate energy-momentum dependence in the matrix element
reduces the discrepancy.Comment: 8 page standard Latex fil
Kosterlitz-Thouless transition in three-state mixed Potts ferro-antiferromagnets
We study three-state Potts spins on a square lattice, in which all bonds are
ferromagnetic along one of the lattice directions, and antiferromagnetic along
the other. Numerical transfer-matrix are used, on infinite strips of width
sites, . Based on the analysis of the ratio of scaled mass
gaps (inverse correlation lengths) and scaled domain-wall free energies, we
provide strong evidence that a critical (Kosterlitz-Thouless) phase is present,
whose upper limit is, in our best estimate, . From analysis
of the (extremely anisotropic) nature of excitations below , we argue that
the critical phase extends all the way down to T=0. While domain walls parallel
to the ferromagnetic direction are soft for the whole extent of the critical
phase, those along the antiferromagnetic direction seem to undergo a softening
transition at a finite temperature. Assuming a bulk correlation length varying,
for , as , , we attempt finite-size scaling plots of our finite-width
correlation lengths. Our best results are for . We propose a
scenario in which such inconsistency is attributed to the extreme narrowness of
the critical region.Comment: 11 pages, 6 .eps figures, LaTeX with IoP macros, to be published in J
Phys
Study of below 1 GeV using Integral Equation Approach
The scattering of is studied using the axial
anomaly, elastic unitarity, analyticity and crossing symmetry. Using the
technique to derive the Roy's equation, an integral equation for the P-wave
amplitude is obtained in terms of the strong P-wave pion pion phase shifts. Its
solution is obtained numerically by an iteration procedure using the starting
point as the solution of the integral equation of the Muskelshsvilli-Omnes
type. It is, however, ambiguous and depends sensitively on the second
derivative of the P-wave amplitude at which cannot directly be
measured.Comment: 26 pages, 10 figure
Multidimensional Gaussian sums arising from distribution of Birkhoff sums in zero entropy dynamical systems
A duality formula, of the Hardy and Littlewood type for multidimensional
Gaussian sums, is proved in order to estimate the asymptotic long time behavior
of distribution of Birkhoff sums of a sequence generated by a skew
product dynamical system on the torus, with zero Lyapounov
exponents. The sequence, taking the values , is pairwise independent
(but not independent) ergodic sequence with infinite range dependence. The
model corresponds to the motion of a particle on an infinite cylinder, hopping
backward and forward along its axis, with a transversal acceleration parameter
. We show that when the parameter is rational then all
the moments of the normalized sums , but the second, are
unbounded with respect to n, while for irrational , with bounded
continuous fraction representation, all these moments are finite and bounded
with respect to n.Comment: To be published in J. Phys.
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