3,299 research outputs found
Diffusion at constant speed in a model phase space
We reconsider the problem of diffusion of particles at constant speed and
present a generalization of the Telegrapher process to higher dimensional
stochastic media (), where the particle can move along directions.
We derive the equations for the probability density function using the
``formulae of differentiation'' of Shapiro and Loginov. The model is an
advancement over similiar models of photon migration in multiply scattering
media in that it results in a true diffusion at constant speed in the limit of
large dimensions.Comment: Final corrected version RevTeX, 6 pages, 1 figur
Near Field Lenses in Two Dimensions
It has been shown that a slab of materials with refractive index = -1 behaves
like a perfect lens focussing all light to an exact electromagnetic copy of an
object. The original lens is limited to producing images the same size as the
object, but here we generalise the concept so that images can be magnified. For
two dimensional systems, over distances much shorter than the free space
wavelength, we apply conformal transformations to the original parallel sided
slab generating a variety of new lenses. Although the new lenses are not
`perfect' they are able to magnify two dimensional objects. The results apply
equally to imaging of electric or magnetic sub wavelength objects in two
dimensions. The concepts have potential applications ranging from microwave
frequencies to the visible.Comment: PDF fil
Imaging the Near Field
In an earlier paper we introduced the concept of the perfect lens which
focuses both near and far electromagnetic fields, hence attaining perfect
resolution. Here we consider refinements of the original prescription designed
to overcome the limitations of imperfect materials. In particular we show that
a multi-layer stack of positive and negative refractive media is less sensitive
to imperfections. It has the novel property of behaving like a fibre-optic
bundle but one that acts on the near field, not just the radiative component.
The effects of retardation are included and minimized by making the slabs
thinner. Absorption then dominates image resolution in the near-field. The
deleterious effects of absorption in the metal are reduced for thinner layers.Comment: RevTeX, (9 pages, 8 figures
Complete controllability of quantum systems
Sufficient conditions for complete controllability of -level quantum
systems subject to a single control pulse that addresses multiple allowed
transitions concurrently are established. The results are applied in particular
to Morse and harmonic-oscillator systems, as well as some systems with
degenerate energy levels. Morse and harmonic oscillators serve as models for
molecular bonds, and the standard control approach of using a sequence of
frequency-selective pulses to address a single transition at a time is either
not applicable or only of limited utility for such systems.Comment: 8 pages, expanded and revised versio
Sub-wavelength imaging at optical frequencies using canalization regime
Imaging with sub-wavelength resolution using a lens formed by periodic
metal-dielectric layered structure is demonstrated. The lens operates in
canalization regime as a transmission device and it does not involve negative
refraction and amplification of evanescent modes. The thickness of the lens
have to be an integer number of half-wavelengths and can be made as large as
required for ceratin applications, in contrast to the other sub-wavelength
lenses formed by metallic slabs which have to be much smaller than the
wavelength. Resolution of at 600 nm wavelength is confirmed by
numerical simulation for a 300 nm thick structure formed by a periodic stack of
10 nm layers of glass with and 5 nm layers of metal-dielectric
composite with . Resolution of is predicted for a
structure with same thickness, period and operating frequency, but formed by
7.76 nm layers of silicon with and 7.24 nm layers of silver with
.Comment: 4 pages, 4 figures, submitted to PR
Power spectrum of mass and activity fluctuations in a sandpile
We consider a directed abelian sandpile on a strip of size ,
driven by adding a grain randomly at the left boundary after every
time-steps. We establish the exact equivalence of the problem of mass
fluctuations in the steady state and the number of zeroes in the ternary-base
representation of the position of a random walker on a ring of size . We
find that while the fluctuations of mass have a power spectrum that varies as
for frequencies in the range , the activity
fluctuations in the same frequency range have a power spectrum that is linear
in .Comment: 8 pages, 10 figure
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