460 research outputs found
Semiclassical Description of Tunneling in Mixed Systems: The Case of the Annular Billiard
We study quantum-mechanical tunneling between symmetry-related pairs of
regular phase space regions that are separated by a chaotic layer. We consider
the annular billiard, and use scattering theory to relate the splitting of
quasi-degenerate states quantized on the two regular regions to specific paths
connecting them. The tunneling amplitudes involved are given a semiclassical
interpretation by extending the billiard boundaries to complex space and
generalizing specular reflection to complex rays. We give analytical
expressions for the splittings, and show that the dominant contributions come
from {\em chaos-assisted}\/ paths that tunnel into and out of the chaotic
layer.Comment: 4 pages, uuencoded postscript file, replaces a corrupted versio
Effective Hamiltonians for some highly frustrated magnets
In prior work, the authors developed a method of degenerate perturbation
theory about the Ising limit to derive an effective Hamiltonian describing
quantum fluctuations in a half-polarized magnetization plateau on the
pyrochlore lattice. Here, we extend this formulation to an arbitrary lattice of
corner sharing simplexes of sites, at a fraction of the
saturation magnetization, with . We present explicit effective
Hamiltonians for the examples of the checkerboard, kagome, and pyrochlore
lattices. The consequent ground states in these cases for are also
discussed.Comment: 10 pages, 2 figures,. Conference proceedings for Highly Frustrated
Magnetism 200
Incremental Optimization Transfer Algorithms: Application to Transmission Tomography
No convergent ordered subsets (OS) type image
reconstruction algorithms for transmission tomography have been
proposed to date. In contrast, in emission tomography, there
are two known families of convergent OS algorithms: methods
that use relaxation parameters (Ahn and Fessler, 2003), and
methods based on the incremental expectation maximization (EM)
approach (Hsiao et al., 2002). This paper generalizes the incremental
EM approach by introducing a general framework that
we call âincremental optimization transfer.â Like incremental EM
methods, the proposed algorithms accelerate convergence speeds
and ensure global convergence (to a stationary point) under mild
regularity conditions without requiring inconvenient relaxation
parameters. The general optimization transfer framework enables
the use of a very broad family of non-EM surrogate functions.
In particular, this paper provides the first convergent OS-type
algorithm for transmission tomography. The general approach is
applicable to both monoenergetic and polyenergetic transmission
scans as well as to other image reconstruction problems. We
propose a particular incremental optimization transfer method
for (nonconcave) penalized-likelihood (PL) transmission image
reconstruction by using separable paraboloidal surrogates (SPS).
Results show that the new âtransmission incremental optimization
transfer (TRIOT)â algorithm is faster than nonincremental
ordinary SPS and even OS-SPS yet is convergent.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85800/1/Fessler200.pd
Quantal Brownian Motion - Dephasing and Dissipation
We analyze quantal Brownian motion in dimensions using the unified model
for diffusion localization and dissipation, and Feynman-Vernon formalism. At
high temperatures the propagator possess a Markovian property and we can write
down an equivalent Master equation. Unlike the case of the
Zwanzig-Caldeira-Leggett model, genuine quantum mechanical effects manifest
themselves due to the disordered nature of the environment. Using Wigner
picture of the dynamics we distinguish between two different mechanisms for
destruction of coherence. The analysis of dephasing is extended to the low
temperature regime by using a semiclassical strategy. Various results are
derived for ballistic, chaotic, diffusive, both ergodic and non-ergodic motion.
We also analyze loss of coherence at the limit of zero temperature and clarify
the limitations of the semiclassical approach. The condition for having
coherent effect due to scattering by low-frequency fluctuations is also pointed
out. It is interesting that the dephasing rate can be either larger or smaller
than the dissipation rate, depending on the physical circumstances.Comment: LaTex, 23 pages, 4 figures, published vesio
Effective Coupling for Open Billiards
We derive an explicit expression for the coupling constants of individual
eigenstates of a closed billiard which is opened by attaching a waveguide. The
Wigner time delay and the resonance positions resulting from the coupling
constants are compared to an exact numerical calculation. Deviations can be
attributed to evanescent modes in the waveguide and to the finite number of
eigenstates taken into account. The influence of the shape of the billiard and
of the boundary conditions at the mouth of the waveguide are also discussed.
Finally we show that the mean value of the dimensionless coupling constants
tends to the critical value when the eigenstates of the billiard follow
random-matrix theory
Convergent Incremental Optimization Transfer Algorithms: Application to Tomography
No convergent ordered subsets (OS) type image reconstruction algorithms for transmission tomography have been proposed to date. In contrast, in emission tomography, there are two known families of convergent OS algorithms: methods that use relaxation parameters , and methods based on the incremental expectation-maximization (EM) approach . This paper generalizes the incremental EM approach by introducing a general framework, "incremental optimization transfer". The proposed algorithms accelerate convergence speeds and ensure global convergence without requiring relaxation parameters. The general optimization transfer framework allows the use of a very broad family of surrogate functions, enabling the development of new algorithms . This paper provides the first convergent OS-type algorithm for (nonconcave) penalized-likelihood (PL) transmission image reconstruction by using separable paraboloidal surrogates (SPS) which yield closed-form maximization steps. We found it is very effective to achieve fast convergence rates by starting with an OS algorithm with a large number of subsets and switching to the new "transmission incremental optimization transfer (TRIOT)" algorithm. Results show that TRIOT is faster in increasing the PL objective than nonincremental ordinary SPS and even OS-SPS yet is convergent.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85980/1/Fessler46.pd
Coin Tossing as a Billiard Problem
We demonstrate that the free motion of any two-dimensional rigid body
colliding elastically with two parallel, flat walls is equivalent to a billiard
system. Using this equivalence, we analyze the integrable and chaotic
properties of this new class of billiards. This provides a demonstration that
coin tossing, the prototypical example of an independent random process, is a
completely chaotic (Bernoulli) problem. The related question of which billiard
geometries can be represented as rigid body systems is examined.Comment: 16 pages, LaTe
First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard
We report on first experimental signatures for chaos-assisted tunneling in a
two-dimensional annular billiard. Measurements of microwave spectra from a
superconducting cavity with high frequency resolution are combined with
electromagnetic field distributions experimentally determined from a normal
conducting twin cavity with high spatial resolution to resolve eigenmodes with
properly identified quantum numbers. Distributions of so-called quasi-doublet
splittings serve as basic observables for the tunneling between whispering
gallery type modes localized to congruent, but distinct tori which are coupled
weakly to irregular eigenstates associated with the chaotic region in phase
space.Comment: 5 pages RevTex, 5 low-resolution figures (high-resolution figures:
http://linac.ikp.physik.tu-darmstadt.de/heiko/chaospub.html, to be published
in Phys. Rev. Let
Ray and wave chaos in asymmetric resonant optical cavities
Optical resonators are essential components of lasers and other
wavelength-sensitive optical devices. A resonator is characterized by a set of
modes, each with a resonant frequency omega and resonance width Delta
omega=1/tau, where tau is the lifetime of a photon in the mode. In a
cylindrical or spherical dielectric resonator, extremely long-lived resonances
are due to `whispering gallery' modes in which light circulates around the
perimeter trapped by total internal reflection. These resonators emit light
isotropically. Recently, a new category of asymmetric resonant cavities (ARCs)
has been proposed in which substantial shape deformation leads to partially
chaotic ray dynamics. This has been predicted to give rise to a universal,
frequency-independent broadening of the whispering-gallery resonances, and
highly anisotropic emission. Here we present solutions of the wave equation for
ARCs which confirm many aspects of the earlier ray-optics model, but also
reveal interesting frequency-dependent effects characteristic of quantum chaos.
For small deformations the lifetime is controlled by evanescent leakage, the
optical analogue of quantum tunneling. We find that the lifetime is much
shortened by a process known as `chaos-assisted tunneling'. In contrast, for
large deformations (~10%) some resonances are found to have longer lifetimes
than predicted by the ray chaos model due to `dynamical localization'.Comment: 4 pages RevTeX with 7 Postscript figure
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