1,438 research outputs found
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
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
Anomalous power law of quantum reversibility for classically regular dynamics
The Loschmidt Echo M(t) (defined as the squared overlap of wave packets
evolving with two slightly different Hamiltonians) is a measure of quantum
reversibility. We investigate its behavior for classically quasi-integrable
systems. A dominant regime emerges where M(t) ~ t^{-alpha} with alpha=3d/2
depending solely on the dimension d of the system. This power law decay is
faster than the result ~ t^{-d} for the decay of classical phase space
densities
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
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
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.
Scale Anomaly and Quantum Chaos in the Billiards with Pointlike Scatterers
We argue that the random-matrix like energy spectra found in pseudointegrable
billiards with pointlike scatterers are related to the quantum violation of
scale invariance of classical analogue system. It is shown that the behavior of
the running coupling constant explains the key characteristics of the level
statistics of pseudointegrable billiards.Comment: 10 pages, RevTex file, uuencode
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
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
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
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