2,007 research outputs found
The Generalized Gutzwiller Method for n=>2 Correlated Orbitals: Itinerant Ferromagnetism in eg-bands
Using the generalized Gutzwiller method we present results on the
ferromagnetic behavior of extended Hubbard models with two degenerate eg
orbitals. We find significant differences to results obtained from Hartree-Fock
theory.Comment: 7 pages in Latex, 3 figures. Accepted for publication in Physica
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
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
Uniform approximations for non-generic bifurcation scenatios including bifurcations of ghost orbits
Gutzwiller's trace formula allows interpreting the density of states of a
classically chaotic quantum system in terms of classical periodic orbits. It
diverges when periodic orbits undergo bifurcations, and must be replaced with a
uniform approximation in the vicinity of the bifurcations. As a characteristic
feature, these approximations require the inclusion of complex ``ghost
orbits''. By studying an example taken from the Diamagnetic Kepler Problem,
viz. the period-quadrupling of the balloon-orbit, we demonstrate that these
ghost orbits themselves can undergo bifurcations, giving rise to non-generic
complicated bifurcation scenarios. We extend classical normal form theory so as
to yield analytic descriptions of both bifurcations of real orbits and ghost
orbit bifurcations. We then show how the normal form serves to obtain a uniform
approximation taking the ghost orbit bifurcation into account. We find that the
ghost bifurcation produces signatures in the semiclassical spectrum in much the
same way as a bifurcation of real orbits does.Comment: 56 pages, 21 figure, LaTeX2e using amsmath, amssymb, epsfig, and
rotating packages. To be published in Annals of Physic
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
Ringing the eigenmodes from compact manifolds
We present a method for finding the eigenmodes of the Laplace operator acting
on any compact manifold. The procedure can be used to simulate cosmic microwave
background fluctuations in multi-connected cosmological models. Other
applications include studies of chaotic mixing and quantum chaos.Comment: 11 pages, 8 figures, IOP format. To be published in the proceedings
of the Cleveland Cosmology and Topology Workshop 17-19 Oct 1997. Submitted to
Class. Quant. Gra
Ab-initio Gutzwiller method: first application to Plutonium
Except for small molecules, it is impossible to solve many electrons systems
without imposing severe approximations. If the configuration interaction
approaches (CI) or Coupled Clusters techniques \cite{FuldeBook} are applicable
for molecules, their generalization for solids is difficult. For materials with
a kinetic energy greater than the Coulomb interaction, calculations based on
the density functional theory (DFT), associated with the local density
approximation (LDA) \cite{Hohenberg64, Kohn65} give satisfying qualitative and
quantitative results to describe ground state properties. These solids have
weakly correlated electrons presenting extended states, like materials or
covalent solids. The application of this approximation to systems where the
wave functions are more localized ( or -states) as transition metals
oxides, heavy fermions, rare earths or actinides is more questionable and can
even lead to unphysical results : for example, insulating FeO and CoO are
predicted to be metalic by the DFT-LDA..
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
Light emission patterns from stadium-shaped semiconductor microcavity lasers
We study light emission patterns from stadium-shaped semiconductor (GaAs)
microcavity lasers theoretically and experimentally. Performing systematic wave
calculations for passive cavity modes, we demonstrate that the averaging by
low-loss modes, such as those realized in multi-mode lasing, generates an
emission pattern in good agreement with the ray model's prediction. In
addition, we show that the dependence of experimental far-field emission
patterns on the aspect ratio of the stadium cavity is well reproduced by the
ray model.Comment: 5 pages, 4 figure
Semiclassical Coherent States propagator
In this work, we derived a semiclassical approximation for the matrix
elements of a quantum propagator in coherent states (CS) basis that avoids
complex trajectories, it only involves real ones. For that propose, we used
the, symplectically invariant, semiclassical Weyl propagator obtained by
performing a stationary phase approximation (SPA) for the path integral in the
Weyl representation. After what, for the transformation to CS representation
SPA is avoided, instead a quadratic expansion of the complex exponent is used.
This procedure also allows to express the semiclassical CS propagator uniquely
in terms of the classical evolution of the initial point, without the need of
any root search typical of Van Vleck Gutzwiller based propagators. For the case
of chaotic Hamiltonian systems, the explicit time dependence of the CS
propagator has been obtained. The comparison with a
\textquotedbl{}realistic\textquotedbl{} chaotic system that derives from a
quadratic Hamiltonian, the cat map, reveals that the expression here derived is
exact up to quadratic Hamiltonian systems.Comment: 13 pages, 2 figure. Accepted for publication in PR
- …