1,047 research outputs found
Analysis of Fourier transform valuation formulas and applications
The aim of this article is to provide a systematic analysis of the conditions
such that Fourier transform valuation formulas are valid in a general
framework; i.e. when the option has an arbitrary payoff function and depends on
the path of the asset price process. An interplay between the conditions on the
payoff function and the process arises naturally. We also extend these results
to the multi-dimensional case, and discuss the calculation of Greeks by Fourier
transform methods. As an application, we price options on the minimum of two
assets in L\'evy and stochastic volatility models.Comment: 26 pages, 3 figures, to appear in Appl. Math. Financ
Combining requirements engineering techniques - theory and case study
© Copyright 2005 IEEEThe selection of requirements engineering (RE) techniques during software project development is a challenge for most developers. One of the reasons is that there is a great lack of requirements engineering education in most academic programs, so software developers have to learn requirements engineering practices on the job. This can easily result in the selection of techniques that are ill-suited for a particular project, as the selection is based on personal preference rather than on the characteristics of the project. Very little research has been done in the area of technique selection based on project attributes. This paper describes research into the selection and combination of RE techniques as well as a case study that applied the selection process to an industrial software project.Li Jiang, Armin Eberlein, Behrouz H. Fa
Vortex in a trapped Bose-Einstein condensate with dipole-dipole interactions
We calculate the critical rotation frequency at which a vortex state becomes
energetically favorable over the vortex-free ground state in a harmonically
trapped Bose-Einstein condensate whose atoms have dipole-dipole interactions as
well as the usual s-wave contact interactions. In the Thomas-Fermi
(hydrodynamic) regime, dipolar condensates in oblate cylindrical traps (with
the dipoles aligned along the axis of symmetry of the trap) tend to have lower
critical rotation frequencies than their purely s-wave contact interaction
counterparts. The converse is true for dipolar condensates in prolate traps.
Quadrupole excitations and centre of mass motion are also briefly discussed as
possible competing mechanisms to a vortex as means by which superfluids with
partially attractive interactions might carry angular momentumComment: 12 pages, 12 figure
Entropy of semiclassical measures for nonpositively curved surfaces
We study the asymptotic properties of eigenfunctions of the Laplacian in the
case of a compact Riemannian surface of nonpositive sectional curvature. We
show that the Kolmogorov-Sinai entropy of a semiclassical measure for the
geodesic flow is bounded from below by half of the Ruelle upper bound. We
follow the same main strategy as in the Anosov case (arXiv:0809.0230). We focus
on the main differences and refer the reader to (arXiv:0809.0230) for the
details of analogous lemmas.Comment: 20 pages. This note provides a detailed proof of a result announced
in appendix A of a previous work (arXiv:0809.0230, version 2
Stress Tensor Correlators in the Schwinger-Keldysh Formalism
We express stress tensor correlators using the Schwinger-Keldysh formalism.
The absence of off-diagonal counterterms in this formalism ensures that the +-
and -+ correlators are free of primitive divergences. We use dimensional
regularization in position space to explicitly check this at one loop order for
a massless scalar on a flat space background. We use the same procedure to show
that the ++ correlator contains the divergences first computed by `t Hooft and
Veltman for the scalar contribution to the graviton self-energy.Comment: 14 pages, LaTeX 2epsilon, no figures, revised for publicatio
Quantum Electrodynamics near a Huttner-Barnett dielectric
We build up a consistent theory of quantum electrodynamics in the presence of
macroscopic polarizable media. We use the Huttner-Barnett model of a dispersive
and absorbing dielectric medium and formulate the theory in terms of
interacting quantum fields. We integrate out the damped polaritons by using
diagrammatic techniques and find an exact expression for the displacement field
(photon) propagator in the presence of a dispersive and absorbing dielectric
half-space. This opens a new route to traceable perturbative calculations of
the same kind as in free-space quantum electrodynamics. As a worked-through
example we consider the interaction of a neutral atom with a dispersive and
absorbing dielectric half-space. For that we use the multipolar coupling
of the atomic dipole moment to the
electromagnetic displacement field. We apply the newly developed formalism to
calculate the one-loop correction to the atomic electron propagator and find
the energy-level shift and changes in the spontaneous decay rates for a neutral
atom close to an absorptive dielectric mirror.Comment: 25 pages, 4 figure
Completeness of evanescent modes in layered dielectrics
In the presence of a dielectric slab, the modes of the free electromagnetic field comprise traveling modes, consisting of incoming, reflected, and transmitted parts, as well as trapped modes that are subject to repeated total internal reflection and emerge as evanescent field outside the slab. Traveling modes have a continuous range of frequencies, but trapped modes occur only at certain discrete frequencies. We solve the problem of which relative weight to use when summing over all modes, as commonly required in perturbative calculations. We demonstrate the correctness of our method by showing the completeness of electromagnetic field modes in the presence of a dielectric slab. We derive a convenient method of summing over all modes by means of a single contour integral, which is very useful in standard quantum electrodynamic calculations
Quantum electrodynamics near anisotropic polarizable materials: Casimir-Polder shifts near multilayers of graphene
In a recent paper, we formulated a theory of nonrelativistic quantum electrodynamics in the presence of an inhomogeneous Huttner-Barnett dielectric. Here we generalize the formalism to anisotropic materials and show how it may be modified to include conducting surfaces. We start with the derivation of the photon propagator for a slab of material and use it to work out the energy-level shift near a medium whose conductivity in the direction parallel to the surface far exceeds that in the direction perpendicular to the surface. We investigate the influence of the anisotropy of the material's electromagnetic response on the Casimir-Polder shifts, both analytically and numerically, and show that it may have a significant impact on the atom-surface interaction, especially in the nonretarded regime, i.e., for small atom-surface separations. Our results for the energy shift may be used to estimate the Casimir-Polder force acting on quantum objects close to multilayers of graphene or graphite. They are particularly important for the case of trapped cold molecules whose dispersive interactions with surfaces often fall within the nonretarded regime where the anisotropy of the material strongly influences the Casimir-Polder force. We also give a formula for the change in the spontaneous decay rate of an excited atom or molecule near an anisotropically conducting surface
The Lake Country Silo
This publication provides detailed instructions to build a Lake County, South Dakota panel silo. The estimated cost of the construction and a list of necessary materials is also provided
Stochastic Spacetime and Brownian Motion of Test Particles
The operational meaning of spacetime fluctuations is discussed. Classical
spacetime geometry can be viewed as encoding the relations between the motions
of test particles in the geometry. By analogy, quantum fluctuations of
spacetime geometry can be interpreted in terms of the fluctuations of these
motions. Thus one can give meaning to spacetime fluctuations in terms of
observables which describe the Brownian motion of test particles. We will first
discuss some electromagnetic analogies, where quantum fluctuations of the
electromagnetic field induce Brownian motion of test particles. We next discuss
several explicit examples of Brownian motion caused by a fluctuating
gravitational field. These examples include lightcone fluctuations, variations
in the flight times of photons through the fluctuating geometry, and
fluctuations in the expansion parameter given by a Langevin version of the
Raychaudhuri equation. The fluctuations in this parameter lead to variations in
the luminosity of sources. Other phenomena which can be linked to spacetime
fluctuations are spectral line broadening and angular blurring of distant
sources.Comment: 15 pages, 3 figures. Talk given at the 9th Peyresq workshop, June
200
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