1,328 research outputs found
Semiclassical Green Function in Mixed Spaces
A explicit formula on semiclassical Green functions in mixed position and
momentum spaces is given, which is based on Maslov's multi-dimensional
semiclassical theory. The general formula includes both coordinate and momentum
representations of Green functions as two special cases of the form.Comment: 8 pages, typeset by Scientific Wor
Comment on "Gravity Waves, Chaos, and Spinning Compact Binaries"
In this comment, I argue that chaotic effects in binary black hole inspiral
will not strongly impact the detection of gravitational waves from such
systems.Comment: 1 page, comment on gr-qc/991004
Exact trace formulae for a class of one-dimensional ray-splitting systems
Based on quantum graph theory we establish that the ray-splitting trace
formula proposed by Couchman {\it et al.} (Phys. Rev. A {\bf 46}, 6193 (1992))
is exact for a class of one-dimensional ray-splitting systems. Important
applications in combinatorics are suggested.Comment: 14 pages, 3 figure
A new vibrational level of the H molecular ion
A new state of the H molecular ion with binding energy of
1.09 a.u. below the first dissociation limit is predicted, using
highly accurate numerical nonrelativistic quantum calculations. It is the first
L=0 excited state, antisymmetric with respect to the exchange of the two
protons. It manifests itself as a huge p-H scattering length of
Bohr radii.Comment: 6 pages + 3 figure
Quantum-to-classical crossover for Andreev billiards in a magnetic field
We extend the existing quasiclassical theory for the superconducting
proximity effect in a chaotic quantum dot, to include a time-reversal-symmetry
breaking magnetic field. Random-matrix theory (RMT) breaks down once the
Ehrenfest time becomes longer than the mean time between
Andreev reflections. As a consequence, the critical field at which the
excitation gap closes drops below the RMT prediction as is
increased. Our quasiclassical results are supported by comparison with a fully
quantum mechanical simulation of a stroboscopic model (the Andreev kicked
rotator).Comment: 11 pages, 10 figure
Periodic orbit quantization of a Hamiltonian map on the sphere
In a previous paper we introduced examples of Hamiltonian mappings with phase
space structures resembling circle packings. It was shown that a vast number of
periodic orbits can be found using special properties. We now use this
information to explore the semiclassical quantization of one of these maps.Comment: 23 pages, REVTEX
Application of the Feshbach-resonance management to a tightly confined Bose-Einstein condensate
We study suppression of the collapse and stabilization of matter-wave
solitons by means of time-periodic modulation of the effective nonlinearity,
using the nonpolynomial Schroedinger equation (NPSE) for BEC trapped in a tight
cigar-shaped potential. By means of systematic simulations, a stability region
is identified in the plane of the modulation amplitude and frequency. In the
low-frequency regime, solitons feature chaotic evolution, although they remain
robust objects.Comment: Physical Review A, in pres
Nano-wires with surface disorder: Giant localization lengths and dynamical tunneling in the presence of directed chaos
We investigate electron quantum transport through nano-wires with one-sided
surface roughness in the presence of a perpendicular magnetic field.
Exponentially diverging localization lengths are found in the
quantum-to-classical crossover regime, controlled by tunneling between regular
and chaotic regions of the underlying mixed classical phase space. We show that
each regular mode possesses a well-defined mode-specific localization length.
We present analytic estimates of these mode localization lengths which agree
well with the numerical data. The coupling between regular and chaotic regions
can be determined by varying the length of the wire leading to intricate
structures in the transmission probabilities. We explain these structures
quantitatively by dynamical tunneling in the presence of directed chaos.Comment: 15 pages, 12 figure
Point perturbations of circle billiards
The spectral statistics of the circular billiard with a point-scatterer is
investigated. In the semiclassical limit, the spectrum is demonstrated to be
composed of two uncorrelated level sequences. The first corresponds to states
for which the scatterer is located in the classically forbidden region and its
energy levels are not affected by the scatterer in the semiclassical limit
while the second sequence contains the levels which are affected by the
point-scatterer. The nearest neighbor spacing distribution which results from
the superposition of these sequences is calculated analytically within some
approximation and good agreement with the distribution that was computed
numerically is found.Comment: 9 pages, 2 figure
Comparing periodic-orbit theory to perturbation theory in the asymmetric infinite square well
An infinite square well with a discontinuous step is one of the simplest
systems to exhibit non-Newtonian ray-splitting periodic orbits in the
semiclassical limit. This system is analyzed using both time-independent
perturbation theory (PT) and periodic-orbit theory and the approximate formulas
for the energy eigenvalues derived from these two approaches are compared. The
periodic orbits of the system can be divided into classes according to how many
times they reflect from the potential step. Different classes of orbits
contribute to different orders of PT. The dominant term in the second-order PT
correction is due to non-Newtonian orbits that reflect from the step exactly
once. In the limit in which PT converges the periodic-orbit theory results
agree with those of PT, but outside of this limit the periodic-orbit theory
gives much more accurate results for energies above the potential step.Comment: 22 pages, 2 figures, 2 tables, submitted to Physical Review
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