3,324 research outputs found
Reconstruction of dielectric constants of multi-layered optical fibers using propagation constants measurements
We present new method for the numerical reconstruction of the variable
refractive index of multi-layered circular weakly guiding dielectric waveguides
using the measurements of the propagation constants of their eigenwaves. Our
numerical examples show stable reconstruction of the dielectric permittivity
function for random noise level using these measurements
Koszul-Tate Cohomology For an Sp(2)-Covariant Quantization of Gauge Theories with Linearly Dependent Generators
The anti-BRST transformation, in its Sp(2)-symmetric version, for the general
case of any stage-reducible gauge theories is implemented in the usual BV
approach. This task is accomplished not by duplicating the gauge symmetries but
rather by duplicating all fields and antifields of the theory and by imposing
the acyclicity of the Koszul-Tate differential. In this way the Sp(2)-covariant
quantization can be realised in the standard BV approach and its equivalence
with BLT quantization can be proven by a special gauge fixing procedure.Comment: 13 pages, Latex, To Be Published in International Journal of Modern
Physics
Harmonic oscillator with nonzero minimal uncertainties in both position and momentum in a SUSYQM framework
In the context of a two-parameter deformation of the
canonical commutation relation leading to nonzero minimal uncertainties in both
position and momentum, the harmonic oscillator spectrum and eigenvectors are
determined by using techniques of supersymmetric quantum mechanics combined
with shape invariance under parameter scaling. The resulting supersymmetric
partner Hamiltonians correspond to different masses and frequencies. The
exponential spectrum is proved to reduce to a previously found quadratic
spectrum whenever one of the parameters , vanishes, in which
case shape invariance under parameter translation occurs. In the special case
where , the oscillator Hamiltonian is shown to coincide
with that of the q-deformed oscillator with and its eigenvectors are
therefore --boson states. In the general case where , the eigenvectors are constructed as linear combinations of
--boson states by resorting to a Bargmann representation of the latter
and to -differential calculus. They are finally expressed in terms of a
-exponential and little -Jacobi polynomials.Comment: LaTeX, 24 pages, no figure, minor changes, additional references,
final version to be published in JP
Hamiltonian BRST-anti-BRST Theory
The hamiltonian BRST-anti-BRST theory is developed in the general case of
arbitrary reducible first class systems. This is done by extending the methods
of homological perturbation theory, originally based on the use of a single
resolution, to the case of a biresolution. The BRST and the anti-BRST
generators are shown to exist. The respective links with the ordinary BRST
formulation and with the -covariant formalism are also established.Comment: 34 pages, Latex fil
Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index
We provide the geometrical meaning of the superconformal index.
With this interpretation, the superconformal index can be realized
as the partition function on a Scherk-Schwarz deformed background. We apply the
localization method in TQFT to compute the deformed partition function since
the deformed action can be written as a -exact form. The
critical points of the deformed action turn out to be the space of flat
connections which are, in fact, zero modes of the gauge field. The one-loop
evaluation over the space of flat connections reduces to the matrix integral by
which the superconformal index is expressed.Comment: 42+1 pages, 2 figures, JHEP style: v1.2.3 minor corrections, v4 major
revision, conclusions essentially unchanged, v5 published versio
Reconstruction of Dielectric Constants of Core and Cladding of Optical Fibers Using Propagation Constants Measurements
Askey-Wilson Type Functions, With Bound States
The two linearly independent solutions of the three-term recurrence relation
of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22],
are slightly modified so as to make it transparent that these functions satisfy
a beautiful symmetry property. It essentially means that the geometric and the
spectral parameters are interchangeable in these functions. We call the
resulting functions the Askey-Wilson functions. Then, we show that by adding
bound states (with arbitrary weights) at specific points outside of the
continuous spectrum of some instances of the Askey-Wilson difference operator,
we can generate functions that satisfy a doubly infinite three-term recursion
relation and are also eigenfunctions of -difference operators of arbitrary
orders. Our result provides a discrete analogue of the solutions of the purely
differential version of the bispectral problem that were discovered in the
pioneering work [8] of Duistermaat and Gr\"unbaum.Comment: 42 pages, Section 3 moved to the end, minor correction
The hybrid meson: new results from the updated mg and alpha_s parameters
We present new results concerning the masses and the decay widths of the most
interesting hybrid meson states taking as inputs the gluon mass mg and the
non-perturbative QCD running coupling constant ?alpha_s(0) comming from both
LQCD and SDE recent estimations.Comment: 10 pages, 8 table
The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields
We consider an "elastic" version of the statistical mechanical monomer-dimer
problem on the n-dimensional integer lattice. Our setting includes the
classical "rigid" formulation as a special case and extends it by allowing each
dimer to consist of particles at arbitrarily distant sites of the lattice, with
the energy of interaction between the particles in a dimer depending on their
relative position. We reduce the free energy of the elastic dimer-monomer (EDM)
system per lattice site in the thermodynamic limit to the moment Lyapunov
exponent (MLE) of a homogeneous Gaussian random field (GRF) whose mean value
and covariance function are the Boltzmann factors associated with the monomer
energy and dimer potential. In particular, the classical monomer-dimer problem
becomes related to the MLE of a moving average GRF. We outline an approach to
recursive computation of the partition function for "Manhattan" EDM systems
where the dimer potential is a weighted l1-distance and the auxiliary GRF is a
Markov random field of Pickard type which behaves in space like autoregressive
processes do in time. For one-dimensional Manhattan EDM systems, we compute the
MLE of the resulting Gaussian Markov chain as the largest eigenvalue of a
compact transfer operator on a Hilbert space which is related to the
annihilation and creation operators of the quantum harmonic oscillator and also
recast it as the eigenvalue problem for a pantograph functional-differential
equation.Comment: 24 pages, 4 figures, submitted on 14 October 2011 to a special issue
of DCDS-
A survey of Hirota's difference equations
A review of selected topics in Hirota's bilinear difference equation (HBDE)
is given. This famous 3-dimensional difference equation is known to provide a
canonical integrable discretization for most important types of soliton
equations. Similarly to the continuous theory, HBDE is a member of an infinite
hierarchy. The central point of our exposition is a discrete version of the
zero curvature condition explicitly written in the form of discrete
Zakharov-Shabat equations for M-operators realized as difference or
pseudo-difference operators. A unified approach to various types of M-operators
and zero curvature representations is suggested. Different reductions of HBDE
to 2-dimensional equations are considered. Among them discrete counterparts of
the KdV, sine-Gordon, Toda chain, relativistic Toda chain and other typical
examples are discussed in detail.Comment: LaTeX, 43 pages, LaTeX figures (with emlines2.sty
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