242 research outputs found
The nodal structure of doubly-excited resonant states of helium
The authors examine the nodal structure of accurate helium wavefunctions calculated by direct diagonalization of the full six-dimensional problem. It is shown that for fixed interelectronic distance R (or hyperspherical radius R) the symmetric doubly-excited resonant states have well defined lambda , mu nodal structure indicating a near separability in prolate spheroidal coordinates. For fixed lambda , however, a clear mixing of R, mu nodes is demonstrated. This corresponds to a breakdown of the adiabatic approximation and can be understood in terms of the classical two-electron motion
Semiclassical initial value calculations of collinear helium atom
Semiclassical calculations using the Herman-Kluk initial value treatment are
performed to determine energy eigenvalues of bound and resonance states of the
collinear helium atom. Both the configuration (where the classical motion
is fully chaotic) and the configuration (where the classical dynamics is
nearly integrable) are treated. The classical motion is regularized to remove
singularities that occur when the electrons collide with the nucleus. Very good
agreement is obtained with quantum energies for bound and resonance states
calculated by the complex rotation method.Comment: 24 pages, 3 figures. Submitted to J. Phys.
Alternative method to find orbits in chaotic systems
We present here a new method which applies well ordered symbolic dynamics to
find unstable periodic and non-periodic orbits in a chaotic system. The method
is simple and efficient and has been successfully applied to a number of
different systems such as the H\'enon map, disk billiards, stadium billiard,
wedge billiard, diamagnetic Kepler problem, colinear Helium atom and systems
with attracting potentials. The method seems to be better than earlier applied
methods.Comment: 5 pages, uuencoded compressed tar PostScript fil
Numerical study of scars in a chaotic billiard
We study numerically the scaling properties of scars in stadium billiard.
Using the semiclassical criterion, we have searched systematically the scars of
the same type through a very wide range, from ground state to as high as the 1
millionth state. We have analyzed the integrated probability density along the
periodic orbit. The numerical results confirm that the average intensity of
certain types of scars is independent of rather than scales with
. Our findings confirm the theoretical predictions of Robnik
(1989).Comment: 7 pages in Revtex 3.1, 5 PS figures available upon request. To appear
in Phys. Rev. E, Vol. 55, No. 5, 199
Statistical properties of energy levels of chaotic systems: Wigner or non-Wigner
For systems whose classical dynamics is chaotic, it is generally believed
that the local statistical properties of the quantum energy levels are well
described by Random Matrix Theory. We present here two counterexamples - the
hydrogen atom in a magnetic field and the quartic oscillator - which display
nearest neighbor statistics strongly different from the usual Wigner
distribution. We interpret the results with a simple model using a set of
regular states coupled to a set of chaotic states modeled by a random matrix.Comment: 10 pages, Revtex 3.0 + 4 .ps figures tar-compressed using uufiles
package, use csh to unpack (on Unix machine), to be published in Phys. Rev.
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Renormalisation in Quantum Mechanics
We study a recently proposed quantum action depending on temperature. We
construct a renormalisation group equation describing the flow of action
parameters with temperature. At zero temperature the quantum action is obtained
analytically and is found free of higher time derivatives. It makes the quantum
action an ideal tool to investigate quantum chaos and quantum instantons.Comment: replaced version with new figs. Text (LaTeX), 3 Figs. (ps
Quantum Chaos in Quantum Wells
We develop a quantitative semiclassical theory for the resosnant tunneling
through a quantum well in a tilted magnetic field. It is shown, that in the
leading semiclassical approximation the tunneling current depends only on
periodic orbits within the quantum well. Further corrections (due to e.g.
"ghost" effect) can be expressed in terms of closed, but non-periodic orbits,
started at the "injection point". The results of the semiclassical theory are
shown to be in good agreement with both the experimental data and numerical
calculations.Comment: 25 pages, 15 figures, accepted for publication in Physica
Significance of Ghost Orbit Bifurcations in Semiclassical Spectra
Gutzwiller's trace formula for the semiclassical density of states in a
chaotic system diverges near bifurcations of periodic orbits, where it must be
replaced with uniform approximations. It is well known that, when applying
these approximations, complex predecessors of orbits created in the bifurcation
("ghost orbits") can produce pronounced signatures in the semiclassical spectra
in the vicinity of the bifurcation. It is the purpose of this paper to
demonstrate that these ghost orbits themselves can undergo bifurcations,
resulting in complex, nongeneric bifurcation scenarios. We do so by studying an
example taken from the Diamagnetic Kepler Problem, viz. the period quadrupling
of the balloon orbit. By application of normal form theory we construct an
analytic description of the complete bifurcation scenario, which is then used
to calculate the pertinent uniform approximation. The ghost orbit bifurcation
turns out to produce signatures in the semiclassical spectrum in much the same
way as a bifurcation of real orbits would.Comment: 20 pages, 6 figures, LATEX (IOP style), submitted to J. Phys.
Structure of Quantum Chaotic Wavefunctions: Ergodicity, Localization, and Transport
We discuss recent developments in the study of quantum wavefunctions and
transport in classically ergodic systems. Surprisingly, short-time classical
dynamics leaves permanent imprints on long-time and stationary quantum
behavior, which are absent from the long-time classical motion. These imprints
can lead to quantum behavior on single-wavelength or single-channel scales
which are very different from random matrix theory expectations. Robust and
quantitative predictions are obtained using semiclassical methods. Applications
to wavefunction intensity statistics and to resonances in open systems are
discussed.Comment: 8 pages, including 2 figures; talk given at `Dynamics of Complex
Systems' workshop in Dresden, 1999 and submitted for conference proceedings
to appear in Physica
Quantum Chaos at Finite Temperature
We use the quantum action to study quantum chaos at finite temperature. We
present a numerical study of a classically chaotic 2-D Hamiltonian system -
harmonic oscillators with anharmonic coupling. We construct the quantum action
non-perturbatively and find temperature dependent quantum corrections in the
action parameters. We compare Poincar\'{e} sections of the quantum action at
finite temperature with those of the classical action.Comment: Text (LaTeX), Figs. (ps
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