7,076 research outputs found
Three-body Casimir-Polder interactions
As part of our program to develop the description of three-body effects in
quantum vacuum phenomena, we study the three-body interaction of two
anisotropically polarizable atoms with a perfect electrically conducting plate,
a generalization of earlier work. Three- and four-scattering effects are
important, and lead to nonmonotonic behavior.Comment: 10 pages, 5 figures, for the proceedings of the conference
Mathematical Structures in Quantum Systems, Benasque, Spain, July 2012, to be
published in Nuovo Ciment
Coloured extension of GL_q(2) and its dual algebra
We address the problem of duality between the coloured extension of the
quantised algebra of functions on a group and that of its quantised universal
enveloping algebra i.e. its dual. In particular, we derive explicitly the
algebra dual to the coloured extension of GL_q(2) using the coloured RLL
relations and exhibit its Hopf structure. This leads to a coloured
generalisation of the R-matrix procedure to construct a bicovariant
differential calculus on the coloured version of GL_q(2). In addition, we also
propose a coloured generalisation of the geometric approach to quantum group
duality given by Sudbery and Dobrev.Comment: 10 pages LaTeX. Talk given at the "XXIII International Colloquium on
Group Theoretical Methods in Physics", July 31 - August 05, 2000, Dubna
(Russia); to appear in the proceeding
How does Casimir energy fall? IV. Gravitational interaction of regularized quantum vacuum energy
Several years ago we demonstrated that the Casimir energy for perfectly
reflecting and imperfectly reflecting parallel plates gravitated normally, that
is, obeyed the equivalence principle. At that time the divergences in the
theory were treated only formally, without proper regularization, and the
coupling to gravity was limited to the canonical energy-momentum-stress tensor.
Here we strengthen the result by removing both of those limitations. We
consider, as a toy model, massless scalar fields interacting with
semitransparent (-function) potentials defining parallel plates, which
become Dirichlet plates for strong coupling. We insert space and time
point-split regulation parameters, and obtain well-defined contributions to the
self- energy of each plate, and the interaction energy between the plates.
(This self-energy does not vanish even in the conformally-coupled,
strong-coupled limit.) We also compute the local energy density, which requires
regularization near the plates. In general, the energy density includes a
surface energy that resides precisely on the boundaries. This energy is also
regulated. The gravitational interaction of this well-defined system is then
investigated, and it is verified that the equivalence principle is satisfied.Comment: 14 pages, 4 figure
Electromagnetic Non-contact Gears: Prelude
We calculate the lateral Lifshitz force between corrugated dielectric slabs
of finite thickness. Taking the thickness of the plates to infinity leads us to
the lateral Lifshitz force between corrugated dielectric surfaces of infinite
extent. Taking the dielectric constant to infinity leads us to the conductor
limit which has been evaluated earlier in the literature.Comment: 7 pages, 2 figures, Contribution to Proceedings of 9th Conference on
Quantum Field Theory Under the Influence of External Conditions (QFEXT09),
Norman, OK, September 21-25, 200
Casimir energy of Sierpinski triangles
Using scaling arguments and the property of self-similarity we derive the
Casimir energies of Sierpinski triangles and Sierpinski rectangles. The
Hausdorff-Besicovitch dimension (fractal dimension) of the Casimir energy is
introduced and the Berry-Weyl conjecture is discussed for these geometries. We
propose that for a class of fractals, comprising of compartmentalized cavities,
it is possible to establish a finite value to the Casimir energy even while the
Casimir energy of the individual cavities consists of divergent terms.Comment: 7 pages, 5 figures, minor typos correcte
How does Casimir energy fall? III. Inertial forces on vacuum energy
We have recently demonstrated that Casimir energy due to parallel plates,
including its divergent parts, falls like conventional mass in a weak
gravitational field. The divergent parts were suitably interpreted as
renormalizing the bare masses of the plates. Here we corroborate our result
regarding the inertial nature of Casimir energy by calculating the centripetal
force on a Casimir apparatus rotating with constant angular speed. We show that
the centripetal force is independent of the orientation of the Casimir
apparatus in a frame whose origin is at the center of inertia of the apparatus.Comment: 8 pages, 2 figures, contribution to QFEXT07 proceeding
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