2,261 research outputs found
Tunnelling in quantum superlattices with variable lacunarity
Quantum fractal superlattices are microelectronic devices consisting of a
series of thin layers of two semiconductor materials deposited alternately on
each other over a substrate following the rules of construction of a fractal
set, here, a symmetrical polyadic Cantor fractal. The scattering properties of
electrons in these superlattices may be modeled by using that of quantum
particles in piecewise constant potential wells. The twist plots representing
the reflection coefficient as function of the lacunarity parameter show the
appearance of black curves with perfectly transparent tunnelling which may be
classified as vertical, arc, and striation nulls. Approximate analytical
formulae for these reflection-less curves are derived using the transfer matrix
method. Comparison with the numerical results show their good accuracy.Comment: 12 pages, 3 figure
Lacunar fractal photon sieves
We present a new family of diffractive lenses whose structure is based on the
combination of two concepts: photon sieve and fractal zone plates with variable
lacunarity. The focusing properties of different members of this family are
examined. It is shown that the sieves provide a smoothing effect on the higher
order foci of a conventional lacunar fractal zone plate. However, the
characteristic self-similar axial response of the fractal zone plates is always
preserved.Comment: 7 pages, 5 figure
Alternate islands of multiple isochronous chains in wave-particle interactions
We analyze the dynamics of a relativistic particle moving in a uniform
magnetic field and perturbed by a standing electrostatic wave. We show that a
pulsed wave produces an infinite number of perturbative terms with the same
winding number, which may generate islands in the same region of phase space.
As a consequence, the number of isochronous island chains varies as a function
of the wave parameters. We observe that in all the resonances, the number of
chains is related to the amplitude of the various resonant terms. We determine
analytically the position of the periodic points and the number of island
chains as a function of the wave number and wave period. Such information is
very important when one is concerned with regular particle acceleration, since
it is necessary to adjust the initial conditions of the particle to obtain the
maximum acceleration.Comment: Submitte
Nontwist non-Hamiltonian systems
We show that the nontwist phenomena previously observed in Hamiltonian
systems exist also in time-reversible non-Hamiltonian systems. In particular,
we study the two standard collision/reconnection scenarios and we compute the
parameter space breakup diagram of the shearless torus. Besides the Hamiltonian
routes, the breakup may occur due to the onset of attractors. We study these
phenomena in coupled phase oscillators and in non-area-preserving maps.Comment: 7 pages, 5 figure
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