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Casimir energy of smooth compact surfaces
We discuss the formalism of Balian and Duplantier for the calculation of the
Casimir energy for an arbitrary smooth compact surface, and use it to give some
examples: a finite cylinder with hemispherical caps, the torus, ellipsoid of
revolution, a "cube" with rounded corners and edges, and a "drum" made of disks
and part of a torus. We propose a model function which approximately captures
the shape dependence of the Casimir energy.Comment: 9 pages, 4 figures, minor changes, published versio
Kelvin-Mach wake in a two-dimensional Fermi sea
The dispersion law for plasma oscillations in a two-dimensional electron gas
in the hydrodynamic approximation interpolates between and dependences as the wave vector increases.
As a result, downstream of a charged impurity in the presence of a uniform
supersonic electric current flow, a wake pattern of induced charge density and
potential is formed whose geometry is controlled by the Mach number . For
the wake consists of transverse wavefronts confined
within a sector whose angle is given by the classic Mach condition. An
additional wake of larger angle resembling the Kelvin ship wake and consistsing
of both transverse and diverging wavefronts is found outside the Mach sector
for . These wakes also trail an external charge traveling
supersonically a fixed distance away from the electron gas.Comment: 4+ pages, 3 figures, minor changes, version to be published in Phys.
Rev. Let
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