804 research outputs found
Domain wall interactions due to vacuum Dirac field fluctuations in 2+1 dimensions
We evaluate quantum effects due to a -component Dirac field in
space-time dimensions, coupled to domain-wall like defects with a smooth shape.
We show that those effects induce non trivial contributions to the
(shape-dependent) energy of the domain walls. For a single defect, we study the
divergences in the corresponding self-energy, and also consider the role of the
massless zero mode, corresponding to the Callan-Harvey mechanism, by coupling
the Dirac field to an external gauge field. For two defects, we show that the
Dirac field induces a non trivial, Casimir-like effect between them, and
provide an exact expression for that interaction in the case of two
straight-line parallel defects. As is the case for the Casimir interaction
energy, the result is finite and unambiguous.Comment: 17 pages, 1 figur
Using boundary methods to compute the Casimir energy
We discuss new approaches to compute numerically the Casimir interaction
energy for waveguides of arbitrary section, based on the boundary methods
traditionally used to compute eigenvalues of the 2D Helmholtz equation. These
methods are combined with the Cauchy's theorem in order to perform the sum over
modes. As an illustration, we describe a point-matching technique to compute
the vacuum energy for waveguides containing media with different
permittivities. We present explicit numerical evaluations for perfect
conducting surfaces in the case of concentric corrugated cylinders and a
circular cylinder inside an elliptic one.Comment: To be published in the Proceedings of QFEXT09, Norman, OK
Vacuum fluctuations and generalized boundary conditions
We present a study of the static and dynamical Casimir effects for a quantum
field theory satisfying generalized Robin boundary condition, of a kind that
arises naturally within the context of quantum circuits. Since those conditions
may also be relevant to measurements of the dynamical Casimir effect, we
evaluate their role in the concrete example of a real scalar field in 1+1
dimensions, a system which has a well-known mechanical analogue involving a
loaded string.Comment: 8 pages, 1 figur
The effect of concurrent geometry and roughness in interacting surfaces
We study the interaction energy between two surfaces, one of them flat, the
other describable as the composition of a small-amplitude corrugation and a
slightly curved, smooth surface. The corrugation, represented by a spatially
random variable, involves Fourier wavelengths shorter than the (local)
curvature radii of the smooth component of the surface. After averaging the
interaction energy over the corrugation distribution, we obtain an expression
which only depends on the smooth component. We then approximate that functional
by means of a derivative expansion, calculating explicitly the leading and
next-to-leading order terms in that approximation scheme. We analyze the
resulting interplay between shape and roughness corrections for some specific
corrugation models in the cases of electrostatic and Casimir interactions.Comment: 14 pages, 3 figure
Derivative expansion for the Casimir effect at zero and finite temperature in dimensions
We apply the derivative expansion approach to the Casimir effect for a real
scalar field in spatial dimensions, to calculate the next to leading order
term in that expansion, namely, the first correction to the proximity force
approximation. The field satisfies either Dirichlet or Neumann boundary
conditions on two static mirrors, one of them flat and the other gently curved.
We show that, for Dirichlet boundary conditions, the next to leading order term
in the Casimir energy is of quadratic order in derivatives, regardless of the
number of dimensions. Therefore it is local, and determined by a single
coefficient. We show that the same holds true, if , for a field which
satisfies Neumann conditions. When , the next to leading order term
becomes nonlocal in coordinate space, a manifestation of the existence of a
gapless excitation (which do exist also for , but produce sub-leading
terms).
We also consider a derivative expansion approach including thermal
fluctuations of the scalar field. We show that, for Dirichlet mirrors, the next
to leading order term in the free energy is also local for any temperature .
Besides, it interpolates between the proper limits: when it tends to
the one we had calculated for the Casimir energy in dimensions, while for
it corresponds to the one for a theory in dimensions,
because of the expected dimensional reduction at high temperatures. For Neumann
mirrors in , we find a nonlocal next to leading order term for any .Comment: 18 pages, 6 figures. Version to appear in Phys. Rev.
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