420 research outputs found
Sonic crystal lenses that obey Lensmaker's formula
This paper presents a theoretical study of the phenomenon of acoustic imaging
by sonic crystals, which are made of two-dimensional regular arrays of rigid
cylinders placed in parallel in air. The scattering of acoustic waves is
computed using the standard multiple scattering theory, and the band structures
are computed by the plane-wave expansion method. It is shown that properly
arranged arrays not only can behave as acoustic lenses, but also the focusing
effect can be well described by Lensmaker's formula. Possible applications are
also discussed.Comment: 4 pages, 5 figure
Approximate Analytic Solution for the Spatiotemporal Evolution of Wave Packets undergoing Arbitrary Dispersion
We apply expansion methods to obtain an approximate expression in terms of
elementary functions for the space and time dependence of wave packets in a
dispersive medium. The specific application to pulses in a cold plasma is
considered in detail, and the explicit analytic formula that results is
provided. When certain general initial conditions are satisfied, these
expressions describe the packet evolution quite well. We conclude by employing
the method to exhibit aspects of dispersive pulse propagation in a cold plasma,
and suggest how predicted and experimental effects may be compared to improve
the theoretical description of a medium's dispersive properties.Comment: 17 pages, 4 figures, RevTe
Quantum shutter approach to tunneling time scales with wave packets
The quantum shutter approach to tunneling time scales (G. Garc\'{\i
}a-Calder\'{o}n and A. Rubio, Phys. Rev. A \textbf{55}, 3361 (1997)), which
uses a cutoff plane wave as the initial condition, is extended in such a way
that a certain type of wave packet can be used as the initial condition. An
analytical expression for the time evolved wave function is derived. The
time-domain resonance, the peaked structure of the probability density (as the
function of time) at the exit of the barrier, originally found with the cutoff
plane wave initial condition, is studied with the wave packet initial
conditions. It is found that the time-domain resonance is not very sensitive to
the width of the packet when the transmission process is in the tunneling
regime.Comment: 6 page
Information hiding and retrieval in Rydberg wave packets using half-cycle pulses
We demonstrate an information hiding and retrieval scheme with the relative
phases between states in a Rydberg wave packet acting as the bits of a data
register. We use a terahertz half-cycle pulse (HCP) to transfer phase-encoded
information from an optically accessible angular momentum manifold to another
manifold which is not directly accessed by our laser pulses, effectively hiding
the information from our optical interferometric measurement techniques. A
subsequent HCP acting on these wave packets reintroduces the information back
into the optically accessible data register manifold which can then be `read'
out.Comment: 4 pages, 4 figure
Quantum Correction in Exact Quantization Rules
An exact quantization rule for the Schr\"{o}dinger equation is presented. In
the exact quantization rule, in addition to , there is an integral term,
called the quantum correction. For the exactly solvable systems we find that
the quantum correction is an invariant, independent of the number of nodes in
the wave function. In those systems, the energy levels of all the bound states
can be easily calculated from the exact quantization rule and the solution for
the ground state, which can be obtained by solving the Riccati equation. With
this new method, we re-calculate the energy levels for the one-dimensional
systems with a finite square well, with the Morse potential, with the symmetric
and asymmetric Rosen-Morse potentials, and with the first and the second
P\"{o}schl-Teller potentials, for the harmonic oscillators both in one
dimension and in three dimensions, and for the hydrogen atom.Comment: 10 pages, no figure, Revte
Optical precursors in transparent media
We theoretically study the linear propagation of a stepwise pulse through a
dilute dispersive medium when the frequency of the optical carrier coincides
with the center of a natural or electromagnetically induced transparency window
of the medium (slow-light systems). We obtain fully analytical expressions of
the entirety of the step response and show that, for parameters representative
of real experiments, Sommerfeld-Brillouin precursors, main field and second
precursors "postcursors" can be distinctly observed, all with amplitudes
comparable to that of the incident step. This behavior strongly contrasts with
that of the systems generally considered up to now
Tunable Vibrational Band Gaps in One-Dimensional Diatomic Granular Crystals with Three-Particle Unit Cells
We investigate the tunable vibration filtering properties of one-dimensional
diatomic granular crystals composed of arrays of stainless steel spheres and
cylinders interacting via Hertzian contact. The arrays consist of periodically
repeated three-particle unit cells (steel-cylinder-sphere) in which the length
of the cylinder is varied systematically. We apply static compression to
linearize the dynamic response of the crystals and characterize their linear
frequency spectrum. We find good agreement between theoretical dispersion
relation analysis (for infinite systems), state-space analysis (for finite
systems), and experiments. We report the observation of up to three distinct
pass bands and two finite band gaps and show their tunability for variations in
cylinder length and static compression
Critical view of WKB decay widths
A detailed comparison of the expressions for the decay widths obtained within
the semiclassical WKB approximation using different approaches to the tunneling
problem is performed. The differences between the available improved formulae
for tunneling near the top and the bottom of the barrier are investigated.
Though the simple WKB method gives the right order of magnitude of the decay
widths, a small number of parameters are often fitted. The need to perform the
fitting procedure remaining consistently within the WKB framework is emphasized
in the context of the fission model based calculations. Calculations for the
decay widths of some recently found super heavy nuclei using microscopic
alpha-nucleus potentials are presented to demonstrate the importance of a
consistent WKB calculation. The half-lives are found to be sensitive to the
density dependence of the nucleon-nucleon interaction and the implementation of
the Bohr-Sommerfeld quantization condition inherent in the WKB approach.Comment: 18 pages, Late
Observing the spin of a free electron
Long ago, Bohr, Pauli, and Mott argued that it is not, in principle, possible to measure the spin components of a free electron. One can try to use a Stern-Gerlach type of device, but the finite size of the beam results in an uncertainty of the splitting force that is comparable with the gradient force. The result is that no definite spin measurement can be made. Recently there has been a revival of interest in this problem, and we will present our own analysis and quantum-mechanical wave-packet calculations which suggest that a spin measurement is possible for a careful choice of initial conditions
The WKB Approximation without Divergences
In this paper, the WKB approximation to the scattering problem is developed
without the divergences which usually appear at the classical turning points. A
detailed procedure of complexification is shown to generate results identical
to the usual WKB prescription but without the cumbersome connection formulas.Comment: 13 pages, TeX file, to appear in Int. J. Theor. Phy
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