1,438 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
Symmetry Decomposition of Chaotic Dynamics
Discrete symmetries of dynamical flows give rise to relations between
periodic orbits, reduce the dynamics to a fundamental domain, and lead to
factorizations of zeta functions. These factorizations in turn reduce the labor
and improve the convergence of cycle expansions for classical and quantum
spectra associated with the flow. In this paper the general formalism is
developed, with the -disk pinball model used as a concrete example and a
series of physically interesting cases worked out in detail.Comment: CYCLER Paper 93mar01
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.
Semiclassical theory of spin-orbit interactions using spin coherent states
We formulate a semiclassical theory for systems with spin-orbit interactions.
Using spin coherent states, we start from the path integral in an extended
phase space, formulate the classical dynamics of the coupled orbital and spin
degrees of freedom, and calculate the ingredients of Gutzwiller's trace formula
for the density of states. For a two-dimensional quantum dot with a spin-orbit
interaction of Rashba type, we obtain satisfactory agreement with fully
quantum-mechanical calculations. The mode-conversion problem, which arose in an
earlier semiclassical approach, has hereby been overcome.Comment: LaTeX (RevTeX), 4 pages, 2 figures, accepted for Physical Review
Letters; final version (v2) for publication with minor editorial change
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
Classical Coulomb three-body problem in collinear eZe configuration
Classical dynamics of two-electron atom and ions H, He, Li,
Be,... in collinear eZe configuration is investigated. It is revealed
that the mass ratio between necleus and electron plays an important role
for dynamical behaviour of these systems. With the aid of analytical tool and
numeircal computation, it is shown that thanks to large mass ratio ,
classical dynamics of these systems is fully chaotic, probably hyperbolic.
Experimental manifestation of this finding is also proposed.Comment: Largely rewritten. 21 pages. All figures are available in
http://ace.phys.h.kyoto-u.ac.jp/~sano/3-body/index.htm
The effect of short ray trajectories on the scattering statistics of wave chaotic systems
In many situations, the statistical properties of wave systems with chaotic
classical limits are well-described by random matrix theory. However,
applications of random matrix theory to scattering problems require
introduction of system specific information into the statistical model, such as
the introduction of the average scattering matrix in the Poisson kernel. Here
it is shown that the average impedance matrix, which also characterizes the
system-specific properties, can be expressed in terms of classical trajectories
that travel between ports and thus can be calculated semiclassically.
Theoretical results are compared with numerical solutions for a model
wave-chaotic system
Nonergodicity of entanglement and its complementary behavior to magnetization in infinite spin chain
We consider the problem of the validity of a statistical mechanical
description of two-site entanglement in an infinite spin chain described by the
XY model Hamiltonian. We show that the two-site entanglement of the state,
evolved from the initial equilibrium state, after a change of the magnetic
field, does not approach its equilibrium value. This suggests that two-site
entanglement, like (single-site) magnetization, is a nonergodic quantity in
this model. Moreover we show that these two nonergodic quantities behave in a
complementary way.Comment: 4 pages, 2 eps figures, RevTeX4; v2: Published versio
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
Stable classical structures in dissipative quantum chaotic systems
We study the stability of classical structures in chaotic systems when a
dissipative quantum evolution takes place. We consider a paradigmatic model,
the quantum baker map in contact with a heat bath at finite temperature. We
analyze the behavior of the purity, fidelity and Husimi distributions
corresponding to initial states localized on short periodic orbits (scar
functions) and map eigenstates. Scar functions, that have a fundamental role in
the semiclassical description of chaotic systems, emerge as very robust against
environmental perturbations. This is confirmed by the study of other states
localized on classical structures. Also, purity and fidelity show a
complementary behavior as decoherence measures.Comment: 4 pages, 3 figure
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