18 research outputs found
Photon density of states for deformed surfaces
A new approach to the Helmholtz spectrum for arbitrarily shaped boundaries
and a rather general class of boundary conditions is introduced. We derive the
boundary induced change of the density of states in terms of the free Green's
function from which we obtain both perturbative and non-perturbative results
for the Casimir interaction between deformed surfaces. As an example, we
compute the lateral electrodynamic Casimir force between two corrugated
surfaces over a wide parameter range. Universal behavior, fixed only by the
largest wavelength component of the surface shape, is identified at large
surface separations. This complements known short distance expansions which are
also reproduced.Comment: 8 pages, J Phys A Special Issue QFEXT0
Parity Doubling and SU(2)_L x SU(2)_R Restoration in the Hadron Spectrum
We construct the most general nonlinear representation of chiral SU(2)_L x
SU(2)_R broken down spontaneously to the isospin SU(2), on a pair of hadrons of
same spin and isospin and opposite parity. We show that any such representation
is equivalent, through a hadron field transformation, to two irreducible
representations on two hadrons of opposite parity with different masses and
axial couplings. This implies that chiral symmetry realized in the
Nambu-Goldstone mode does not predict the existence of degenerate multiplets of
hadrons of opposite parity nor any relations between their couplings or masses.Comment: 4 pages, 1 figure; v3: Note added to clarify implications for hadrons
that do not couple to pions: Chiral symmetry can be realized linearly on such
states, leading to parity doubling. To the extent that they are parity
doubled, these hadrons must decouple from pions, a striking prediction that
can be tested experimentally. This applies to the work of L. Glozman and
collaborator
The Casimir Energy for a Hyperboloid Facing a Plate in the Optical Approximation
We study the Casimir energy of a massless scalar field that obeys Dirichlet
boundary conditions on a hyperboloid facing a plate. We use the optical
approximation including the first six reflections and compare the results with
the predictions of the proximity force approximation and the semi-classical
method. We also consider finite size effects by contrasting the infinite with a
finite plate. We find sizable and qualitative differences between the new
optical method and the more traditional approaches.Comment: v2: 14 pages, 11 eps figures; typo in eq. (21) removed, clarification
added, fig. 10 improved; version published in Phys. Rev.
Casimir interaction between a plate and a cylinder
We find the exact Casimir force between a plate and a cylinder, a geometry
intermediate between parallel plates, where the force is known exactly, and the
plate--sphere, where it is known at large separations. The force has an
unexpectedly weak decay \sim L/(H^3 \ln(H/R)) at large plate--cylinder
separations H (L and R are the cylinder length and radius), due to transverse
magnetic modes. Path integral quantization with a partial wave expansion
additionally gives a qualitative difference for the density of states of
electric and magnetic modes, and corrections at finite temperatures.Comment: 4 pages, 3 figure
Attractive Casimir Forces in a Closed Geometry
We study the Casimir force acting on a conducting piston with arbitrary cross
section. We find the exact solution for a rectangular cross section and the
first three terms in the asymptotic expansion for small height to width ratio
when the cross section is arbitrary. Though weakened by the presence of the
walls, the Casimir force turns out to be always attractive. Claims of repulsive
Casimir forces for related configurations, like the cube, are invalidated by
cutoff dependence.Comment: An updated version to coincide with the one published December 2005
in PRL. 4 pages, 2 figure
Casimir interaction: pistons and cavity
The energy of a perfectly conducting rectangular cavity is studied by making
use of pistons' interactions. The exact solution for a 3D perfectly conducting
piston with an arbitrary cross section is being discussed.Comment: 10 pages, 2 figures, latex2
Comment on the sign of the Casimir force
I show that reflection positivity implies that the force between any mirror
pair of charge-conjugate probes of the quantum vacuum is attractive. This
generalizes a recent theorem of Kenneth and Klich to interacting quantum
fields, to arbitrary semiclassical bodies, and to quantized probes with
non-overlapping wavefunctions. I also prove that the torques on
charge-conjugate probes tend always to rotate them into a mirror-symmetric
position.Comment: 13 pages, 1 figure, Latex file. Several points clarified and
expanded, two references added
Casimir Force on a Micrometer Sphere in a Dip: Proposal of an Experiment
The attractive Casimir force acting on a micrometer-sphere suspended in a
spherical dip, close to the wall, is discussed. This setup is in principle
directly accessible to experiment. The sphere and the substrate are assumed to
be made of the same perfectly conducting material.Comment: 11 pages, 1 figure; to appear in J. Phys. A: Math. Ge
Casimir forces between cylinders and plates
We study collective interaction effects that result from the change of free
quantum electrodynamic field fluctuations by one- and two-dimensional perfect
metal structures. The Casimir interactions in geometries containing plates and
cylinders is explicitly computed using partial wave expansions of constrained
path integrals. We generalize previously obtained results and provide a more
detailed description of the technical aspects of the approach \cite{Emig06}. We
find that the interactions involving cylinders have a weak logarithmic
dependence on the cylinder radius, reflecting that one-dimensional
perturbations are marginally relevant in 4D space-time. For geometries
containing two cylinders and one or two plates, we confirm a previously found
non-monotonic dependence of the interaction on the object's separations which
does not follow from pair-wise summation of two-body forces. Qualitatively,
this effect is explained in terms of fluctuating charges and currents and their
mirror images