31,763 research outputs found
Distinguishability revisited: depth dependent bounds on reconstruction quality in electrical impedance tomography
The reconstruction problem in electrical impedance tomography is highly
ill-posed, and it is often observed numerically that reconstructions have poor
resolution far away from the measurement boundary but better resolution near
the measurement boundary. The observation can be quantified by the concept of
distinguishability of inclusions. This paper provides mathematically rigorous
results supporting the intuition. Indeed, for a model problem lower and upper
bounds on the distinguishability of an inclusion are derived in terms of the
boundary data. These bounds depend explicitly on the distance of the inclusion
to the boundary, i.e. the depth of the inclusion. The results are obtained for
disk inclusions in a homogeneous background in the unit disk. The theoretical
bounds are verified numerically using a novel, exact characterization of the
forward map as a tridiagonal matrix.Comment: 25 pages, 6 figure
A Conformal Truncation Framework for Infinite-Volume Dynamics
We present a new framework for studying conformal field theories deformed by
one or more relevant operators. The original CFT is described in infinite
volume using a basis of states with definite momentum, , and conformal
Casimir, . The relevant deformation is then considered using
lightcone quantization, with the resulting Hamiltonian expressed in terms of
this CFT basis. Truncating to states with , one can numerically find the resulting spectrum, as well
as other dynamical quantities, such as spectral densities of operators. This
method requires the introduction of an appropriate regulator, which can be
chosen to preserve the conformal structure of the basis. We check this
framework in three dimensions for various perturbative deformations of a free
scalar CFT, and for the case of a free CFT deformed by a mass term and a
non-perturbative quartic interaction at large-. In all cases, the truncation
scheme correctly reproduces known analytic results. We also discuss a general
procedure for generating a basis of Casimir eigenstates for a free CFT in any
number of dimensions.Comment: 48+37 pages, 17 figures; v2: references added, small clarification
Measuring the Atmospheric Influence on Differential Astrometry: a Simple Method Applied to Wide Field CCD Frames
Sets of short exposure, guided CCD frames are used to measure the noise added
by the atmosphere to differential astrometric observations. Large nightly
variations that are correlated with the seeing have been found in the data
obtained over 2 years at the KPNO and CTIO 0.9-meter telescopes. The rms noise
added by the atmosphere, after a linear transformation of the raw data,
is found to be 3 to 7 mas, normalized to 100 seconds exposure time and a field
of view of 20 arcminutes near the zenith. An additional nearly constant noise
(base-level) of 8.5 mas = 0.012 pixel is found for the KPNO and 6.0 mas = 0.015
pixel for the CTIO telescope. This implies that a ground-based, all sky,
astrometric survey from guided CCD frames is more likely limited by the
base-level noise than by the atmosphere and could reach an accuracy better than
10 mas under good seeing conditions.Comment: 12 pages LaTeX incl. tables, no figures, accepted by PASP, scheduled
for Dec.9
Duality-invariant Quantum Field Theories of Charges and Monopoles
We present a manifestly Lorentz- and SO(2)-Duality-invariant local Quantum
Field Theory of electric charges, Dirac magnetic monopoles and dyons. The
manifest invariances are achieved by means of the PST-mechanism. The dynamics
for classical point particles is described by an action functional living on a
circle, if the Dirac-Schwinger quantization condition for electric and magnetic
charges holds. The inconsistent classical field theory depends on an arbitrary,
but fixed, external vector field, a generalization of the Dirac-string.
Nevertheless, the Quantum Field Theory, obtained from this classical action via
a functional integral approach, turns out to be independent of the particular
vector field chosen, and thus consistent, if the Dirac-Schwinger quantization
condition holds. We provide explicit expressions for the generating functionals
of observables, proving that they are Dirac-string independent. Since
Lorentz-invariance is manifest at each step, the quantum theory admits also a
manifestly diffeomorphism invariant coupling to external gravity. Relations
with previous formulations, and with SO(2)--non invariant theories are
clarified.Comment: 49 pages, LaTeX, no figure
Geometry and symmetries of multi-particle systems
The quantum dynamical evolution of atomic and molecular aggregates, from
their compact to their fragmented states, is parametrized by a single
collective radial parameter. Treating all the remaining particle coordinates in
d dimensions democratically, as a set of angles orthogonal to this collective
radius or by equivalent variables, bypasses all independent-particle
approximations. The invariance of the total kinetic energy under arbitrary
d-dimensional transformations which preserve the radial parameter gives rise to
novel quantum numbers and ladder operators interconnecting its eigenstates at
each value of the radial parameter.
We develop the systematics and technology of this approach, introducing the
relevant mathematics tutorially, by analogy to the familiar theory of angular
momentum in three dimensions. The angular basis functions so obtained are
treated in a manifestly coordinate-free manner, thus serving as a flexible
generalized basis for carrying out detailed studies of wavefunction evolution
in multi-particle systems.Comment: 37 pages, 2 eps figure
Hamiltonian Dynamics of Linearly Polarized Gowdy Models Coupled to Massless Scalar Fields
The purpose of this paper is to analyze in detail the Hamiltonian formulation
for the compact Gowdy models coupled to massless scalar fields as a necessary
first step towards their quantization. We will pay special attention to the
coupling of matter and those features that arise for the three-handle and
three-sphere topologies that are not present in the well studied three torus
case -in particular the polar constraints that come from the regularity
conditions on the metric. As a byproduct of our analysis we will get an
alternative understanding, within the Hamiltonian framework, of the appearance
of initial and final singularities for these models.Comment: Final version to appear in Classical and Quantum Gravit
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