462 research outputs found
On the Vacuum energy of a Color Magnetic Vortex
We calculate the one loop gluon vacuum energy in the background of a color
magnetic vortex for SU(2) and SU(3). We use zeta functional regularization to
obtain analytic expressions suitable for numerical treatment. The momentum
integration is turned to the imaginary axis and fast converging sums/integrals
are obtained. We investigate numerically a number of profiles of the
background. In each case the vacuum energy turns out to be positive increasing
in this way the complete energy and making the vortex configuration less
stable. In this problem bound states (tachyonic modes) are present for all
investigated profiles making them intrinsically unstable.Comment: 28 pages, 4 figure
Study of the risk-adjusted pricing methodology model with methods of Geometrical Analysis
Families of exact solutions are found to a nonlinear modification of the
Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM)
incorporates both transaction costs and the risk from a volatile portfolio.
Using the Lie group analysis we obtain the Lie algebra admitted by the RAPM
equation. It gives us the possibility to describe an optimal system of
subalgebras and correspondingly the set of invariant solutions to the model. In
this way we can describe the complete set of possible reductions of the
nonlinear RAPM model. Reductions are given in the form of different second
order ordinary differential equations. In all cases we provide solutions to
these equations in an exact or parametric form. We discuss the properties of
these reductions and the corresponding invariant solutions.Comment: larger version with exact solutions, corrected typos, 13 pages,
Symposium on Optimal Stopping in Abo/Turku 200
Investigation of dynamical systems using tools of the theory of invariants and projective geometry
The investigation of nonlinear dynamical systems of the type
by means of reduction to
some ordinary differential equations of the second order in the form
is done. The main
backbone of this investigation was provided by the theory of invariants
developed by S. Lie, R. Liouville and A. Tresse at the end of the 19th century
and the projective geometry of E. Cartan. In our work two, in some sense
supplementary, systems are considered: the Lorenz system and the R\"o\ss ler system
. The invarinats for the ordinary
differential equations, which correspond to the systems mentioned abouve, are
evaluated. The connection of values of the invariants with characteristics of
dynamical systems is established.Comment: 18 pages, Latex, to appear in J. of Applied Mathematics (ZAMP
The low temperature corrections to the Casimir force between a sphere and a plane
We calculate the low temperature corrections to the free energy for a sphere
in front of a plane. First, the scalar field obeying Dirichet or Neumann
boundary conditions is considered. Second, the electromagnetic field is
studied, the sphere being perfectly conducting and being a dielectric ball with
both, constant permittivity and permittivity of the plasma model.Comment: Submitted to the proceedings of the Workshop "Cosmology, Quantum
Vacuum and Zeta Functions", Universitat Aut\`onoma de Barcelona, 8-10th
March, 2010; 12 pages, 5 figure
Gravitational effects on a rigid Casimir cavity
Vacuum fluctuations produce a force acting on a rigid Casimir cavity in a
weak gravitational field. Such a force is here evaluated and is found to have
opposite direction with respect to the gravitational acceleration; the order of
magnitude for a multi-layer cavity configuration is analyzed and experimental
detection is discussed, bearing in mind the current technological resources.Comment: 7 pages, Latex. Talk given at the Fifth Leipzig Workshop on Quantum
Field Theory under the Influence of External Conditions, September 200
Casimir effect between moving branes
We consider a supersymmetric model with a single matter supermultiplet in a
five-dimensional space-time with orbifold compactification along the fifth
dimension. The boundary conditions on the two orbifold planes are chosen in
such a way that supersymmetry remains unbroken on the boundaries. We calculate
the vacuum energy-momentum tensor in a configuration in which the boundary
branes are moving with constant velocity. The results show that the
contribution from fermions cancels that of bosons only in the static limit, but
in general a velocity-dependent Casimir energy arises between the branes. We
relate this effect to the particle production due to the branes motion and
finally we discuss some cosmological consequences.Comment: 14 pages, LaTeX. Final version with new references included, to be
published in Nucl. Phys.
Comment on "Temperature dependence of the Casimir force for lossy bulk media"
Recently Yampol'skii et al. [Phys. Rev. A v.82, 032511 (2010)] advocated that
Lifshitz theory is not applicable when the characteristic wavelength of the
fluctuating electromagnetic field, responsible for the thermal correction to
the Casimir force, is larger than the size of the metal test bodies. It was
claimed that this is the case in experiments which exclude Lifshitz theory
combined with the Drude model. We calculate the wavelengths of the evanescent
waves giving the dominant contribution to the thermal correction and we find
that they are much smaller than the sizes of the test bodies. The opposite
conclusion obtained by the authors arose from a confusion between propagating
and evanescent waves.Comment: 3 page
Vacuum fluctuation force on a rigid Casimir cavity in a gravitational field
We discuss the possibility of verifying the equivalence principle for the
zero-point energy of quantum electrodynamics, by evaluating the force, produced
by vacuum fluctuations, acting on a rigid Casimir cavity in a weak
gravitational field. The resulting force has opposite direction with respect to
the gravitational acceleration; the order of magnitude for a multi-layer cavity
configuration is derived and experimental feasibility is discussed, taking into
account current technological resources.Comment: 13 pages, Latex. In the revised version, the presentation has been
improve
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