2,329 research outputs found
Closed orbits and spatial density oscillations in the circular billiard
We present a case study for the semiclassical calculation of the oscillations
in the particle and kinetic-energy densities for the two-dimensional circular
billiard. For this system, we can give a complete classification of all closed
periodic and non-periodic orbits. We discuss their bifurcations under variation
of the starting point r and derive analytical expressions for their properties
such as actions, stability determinants, momentum mismatches and Morse indices.
We present semiclassical calculations of the spatial density oscillations using
a recently developed closed-orbit theory [Roccia J and Brack M 2008 Phys. Rev.
Lett. 100 200408], employing standard uniform approximations from perturbation
and bifurcation theory, and test the convergence of the closed-orbit sum.Comment: LaTeX, 42 pp., 17 figures (24 *.eps files, 1 *.tex file); final
version (v3) to be published in J. Phys.
On the canonically invariant calculation of Maslov indices
After a short review of various ways to calculate the Maslov index appearing
in semiclassical Gutzwiller type trace formulae, we discuss a
coordinate-independent and canonically invariant formulation recently proposed
by A Sugita (2000, 2001). We give explicit formulae for its ingredients and
test them numerically for periodic orbits in several Hamiltonian systems with
mixed dynamics. We demonstrate how the Maslov indices and their ingredients can
be useful in the classification of periodic orbits in complicated bifurcation
scenarios, for instance in a novel sequence of seven orbits born out of a
tangent bifurcation in the H\'enon-Heiles system.Comment: LaTeX, 13 figures, 3 tables, submitted to J. Phys.
Semiclassical Theory of Time-Reversal Focusing
Time reversal mirrors have been successfully implemented for various kinds of
waves propagating in complex media. In particular, acoustic waves in chaotic
cavities exhibit a refocalization that is extremely robust against external
perturbations or the partial use of the available information. We develop a
semiclassical approach in order to quantitatively describe the refocusing
signal resulting from an initially localized wave-packet. The time-dependent
reconstructed signal grows linearly with the temporal window of injection, in
agreement with the acoustic experiments, and reaches the same spatial extension
of the original wave-packet. We explain the crucial role played by the chaotic
dynamics for the reconstruction of the signal and its stability against
external perturbations.Comment: 4 pages, 1 figur
Semiclassical description of shell effects in finite fermion systems
A short survey of the semiclassical periodic orbit theory, initiated by M.
Gutzwiller and generalized by many other authors, is given. Via so-called
semiclassical trace formmulae, gross-shell effects in bound fermion systems can
be interpreted in terms of a few periodic orbits of the corresponding classical
systems. In integrable systems, these are usually the shortest members of the
most degenerate families or orbits, but in some systems also less degenerate
orbits can determine the gross-shell structure. Applications to nuclei, metal
clusters, semiconductor nanostructures, and trapped dilute atom gases are
discussed.Comment: LaTeX (revteX4) 6 pages; invited talk at Int. Conference "Finite
Fermionic Systems: Nilsson Model 50 Years", Lund, Sweden, June 14-18, 200
Analytical perturbative approach to periodic orbits in the homogeneous quartic oscillator potential
We present an analytical calculation of periodic orbits in the homogeneous
quartic oscillator potential. Exploiting the properties of the periodic
Lam{\'e} functions that describe the orbits bifurcated from the fundamental
linear orbit in the vicinity of the bifurcation points, we use perturbation
theory to obtain their evolution away from the bifurcation points. As an
application, we derive an analytical semiclassical trace formula for the
density of states in the separable case, using a uniform approximation for the
pitchfork bifurcations occurring there, which allows for full semiclassical
quantization. For the non-integrable situations, we show that the uniform
contribution of the bifurcating period-one orbits to the coarse-grained density
of states competes with that of the shortest isolated orbits, but decreases
with increasing chaoticity parameter .Comment: 15 pages, LaTeX, 7 figures; revised and extended version, to appear
in J. Phys. A final version 3; error in eq. (33) corrected and note added in
prin
Absolute Calibration of a Large-diameter Light Source
A method of absolute calibration for large aperture optical systems is
presented, using the example of the Pierre Auger Observatory fluorescence
detectors. A 2.5 m diameter light source illuminated by an ultra--violet light
emitting diode is calibrated with an overall uncertainty of 2.1 % at a
wavelength of 365 nm.Comment: 15 pages, 8 figures. Submitted to JINS
Absolute Calibration of the Auger Fluorescence Detectors
Absolute calibration of the Pierre Auger Observatory fluorescence detectors
uses a light source at the telescope aperture. The technique accounts for the
ombined effects of all detector components in a single measurement. The
calibrated 2.5 m diameter light source fills the aperture, providing uniform
illumination to each pixel. The known flux from the light source and the
response of the acquisition system give the required calibration for each
pixel. In the lab, light source uniformity is studied using CCD images and the
intensity is measured relative to NIST-calibrated photodiodes. Overall
uncertainties are presently 12%, and are dominated by systematics.Comment: 4 pages, 3 figure. Submitted to the 29th ICRC, Pune, Indi
Uniform semiclassical trace formula for U(3) --> SO(3) symmetry breaking
We develop a uniform semiclassical trace formula for the density of states of
a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term
. This term breaks the U(3) symmetry of the HO, resulting in a
spherical system with SO(3) symmetry. We first treat the anharmonic term in
semiclassical perturbation theory by integration of the action of the perturbed
periodic HO orbits over the manifold P which characterizes
their 4-fold degeneracy. Then we obtain an analytical uniform trace formula
which in the limit of strong perturbations (or high energy) asymptotically goes
over into the correct trace formula of the full anharmonic system with SO(3)
symmetry, and in the limit (or energy) restores the HO trace
formula with U(3) symmetry. We demonstrate that the gross-shell structure of
this anharmonically perturbed system is dominated by the two-fold degenerate
diameter and circular orbits, and {\it not} by the orbits with the largest
classical degeneracy, which are the three-fold degenerate tori with rational
ratios of radial and angular frequencies. The same
holds also for the limit of a purely quartic spherical potential .Comment: LaTeX (revtex4), 26pp., 5 figures, 1 table; final version to be
published in J. Phys. A (without appendices C and D
Occurrence of periodic Lam\'e functions at bifurcations in chaotic Hamiltonian systems
We investigate cascades of isochronous pitchfork bifurcations of
straight-line librating orbits in some two-dimensional Hamiltonian systems with
mixed phase space. We show that the new bifurcated orbits, which are
responsible for the onset of chaos, are given analytically by the periodic
solutions of the Lam\'e equation as classified in 1940 by Ince. In Hamiltonians
with C_ symmetry, they occur alternatingly as Lam\'e functions of period
2K and 4K, respectively, where 4K is the period of the Jacobi elliptic function
appearing in the Lam\'e equation. We also show that the two pairs of orbits
created at period-doubling bifurcations of touch-and-go type are given by two
different linear combinations of algebraic Lam\'e functions with period 8K.Comment: LaTeX2e, 22 pages, 14 figures. Version 3: final form of paper,
accepted by J. Phys. A. Changes in Table 2; new reference [25]; name of
bifurcations "touch-and-go" replaced by "island-chain
Uniform approximations for pitchfork bifurcation sequences
In non-integrable Hamiltonian systems with mixed phase space and discrete
symmetries, sequences of pitchfork bifurcations of periodic orbits pave the way
from integrability to chaos. In extending the semiclassical trace formula for
the spectral density, we develop a uniform approximation for the combined
contribution of pitchfork bifurcation pairs. For a two-dimensional double-well
potential and the familiar H\'enon-Heiles potential, we obtain very good
agreement with exact quantum-mechanical calculations. We also consider the
integrable limit of the scenario which corresponds to the bifurcation of a
torus from an isolated periodic orbit. For the separable version of the
H\'enon-Heiles system we give an analytical uniform trace formula, which also
yields the correct harmonic-oscillator SU(2) limit at low energies, and obtain
excellent agreement with the slightly coarse-grained quantum-mechanical density
of states.Comment: LaTeX, 31 pp., 18 figs. Version (v3): correction of several misprint
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