807 research outputs found
Unitary Equivalence of the Metric and Holonomy Formulations of 2+1 Dimensional Quantum Gravity on the Torus
Recent work on canonical transformations in quantum mechanics is applied to
transform between the Moncrief metric formulation and the Witten-Carlip
holonomy formulation of 2+1-dimensional quantum gravity on the torus. A
non-polynomial factor ordering of the classical canonical transformation
between the metric and holonomy variables is constructed which preserves their
classical modular transformation properties. An extension of the definition of
a unitary transformation is briefly discussed and is used to find the inner
product in the holonomy variables which makes the canonical transformation
unitary. This defines the Hilbert space in the Witten-Carlip formulation which
is unitarily equivalent to the natural Hilbert space in the Moncrief
formulation. In addition, gravitational theta-states arising from ``large''
diffeomorphisms are found in the theory.Comment: 31 pages LaTeX [Important Revision: a section is added constructing
the inner product/Hilbert space for the Witten-Carlip holonomy formulation;
the proof of unitary equivalence of the metric and holonomy formulations is
then completed. Other additions include discussion of relation of canonical
and unitary transformations. Title/abstract change.
Classical phase space and statistical mechanics of identical particles
Starting from the quantum theory of identical particles, we show how to
define a classical mechanics that retains information about the quantum
statistics. We consider two examples of relevance for the quantum Hall effect:
identical particles in the lowest Landau level, and vortices in the
Chern-Simons Ginzburg-Landau model. In both cases the resulting {\em classical}
statistical mechanics is shown to be a nontrivial classical limit of Haldane's
exclusion statistics.Comment: 40 pages, Late
Determination of metal speciation in solution phase of biosolid and contaminated soil via VisualMinteq Model and Donnan Membrane Technique
Extended abstract.Trang Huynh, Alan Baker, Mike McLaughlin, Scott Laidlaw and David Gregor
Are All Particles Identical?
We consider the possibility that all particles in the world are fundamentally
identical, i.e., belong to the same species. Different masses, charges, spins,
flavors, or colors then merely correspond to different quantum states of the
same particle, just as spin-up and spin-down do. The implications of this
viewpoint can be best appreciated within Bohmian mechanics, a precise
formulation of quantum mechanics with particle trajectories. The implementation
of this viewpoint in such a theory leads to trajectories different from those
of the usual formulation, and thus to a version of Bohmian mechanics that is
inequivalent to, though arguably empirically indistinguishable from, the usual
one. The mathematical core of this viewpoint is however rather independent of
the detailed dynamical scheme Bohmian mechanics provides, and it amounts to the
assertion that the configuration space for N particles, even N
``distinguishable particles,'' is the set of all N-point subsets of physical
3-space.Comment: 12 pages LaTeX, no figure
Case studies and evidence-based approaches to addressing urban soil lead contamination
Urban soils in many communities in the United States and internationally have been contaminated by lead (Pb) from past use of lead additives in gasoline, deterioration of exterior paint, emissions from Pb smelters and battery recycling and other industries. Exposure to Pb in soil and related dust is widespread in many inner city areas. Up to 20–40% of urban children in some neighborhoods have blood lead levels (BLLs) equal to or above 5 μg per decilitre, the reference level of health concern by the U.S. Centers for Disease Control. Given the widespread nature of Pb contamination in urban soils it has proven a challenge to reduce exposure. In order to prevent this exposure, an evidence-based approach is required to isolate or remediate the soils and prevent children and adult's ongoing exposure. To date, the majority of community soil Pb remediation efforts have been focused in mining towns or in discrete neighborhoods where Pb smelters have impacted communities. These efforts have usually entailed very expensive dig and dump soil Pb remediation techniques, funded by the point source polluters. Remediating widespread non-point source urban soil contamination using this approach is neither economical nor feasible from a practical standpoint. Despite the need to remediate/isolate urban soils in inner city areas, no deliberate, large scale, cost effective Pb remediation schemes have been implemented to isolate inner city soils impacted from sources other than mines and smelters. However, a city-wide natural experiment of flooding in New Orleans by Hurricane Katrina demonstrated that declines in soil Pb resulted in major BLL reductions. Also a growing body of literature of smaller scale pilot studies and programs does exist regarding low cost efforts to isolate Pb contaminated urban soils. This paper reviews the literature regarding the effectiveness of soil Pb remediation for reducing Pb exposure and BLL in children, and suggests best practices for addressing the epidemics of low-level Pb poisoning occurring in many inner city areas
Analytic Representation of Finite Quantum Systems
A transform between functions in R and functions in Zd is used to define the
analogue of number and coherent states in the context of finite d-dimensional
quantum systems. The coherent states are used to define an analytic
representation in terms of theta functions. All states are represented by
entire functions with growth of order 2, which have exactly d zeros in each
cell. The analytic function of a state is constructed from its zeros. Results
about the completeness of finite sets of coherent states within a cell are
derived
Vortices on Higher Genus Surfaces
We consider the topological interactions of vortices on general surfaces. If
the genus of the surface is greater than zero, the handles can carry magnetic
flux. The classical state of the vortices and the handles can be described by a
mapping from the fundamental group to the unbroken gauge group. The allowed
configurations must satisfy a relation induced by the fundamental group. Upon
quantization, the handles can carry ``Cheshire charge.'' The motion of the
vortices can be described by the braid group of the surface. How the motion of
the vortices affects the state is analyzed in detail.Comment: 28 pages with 10 figures; uses phyzzx and psfig; Caltech preprint
CALT-68-187
No-Boundary Theta-Sectors in Spatially Flat Quantum Cosmology
Gravitational theta-sectors are investigated in spatially locally homogeneous
cosmological models with flat closed spatial surfaces in 2+1 and 3+1 spacetime
dimensions. The metric ansatz is kept in its most general form compatible with
Hamiltonian minisuperspace dynamics. Nontrivial theta-sectors admitting a
semiclassical no-boundary wave function are shown to exist only in 3+1
dimensions, and there only for two spatial topologies. In both cases the
spatial surface is nonorientable and the nontrivial no-boundary theta-sector
unique. In 2+1 dimensions the nonexistence of nontrivial no-boundary
theta-sectors is shown to be of topological origin and thus to transcend both
the semiclassical approximation and the minisuperspace ansatz. Relation to the
necessary condition given by Hartle and Witt for the existence of no-boundary
theta-states is discussed.Comment: 30 p
Testing spatial noncommutativiy via the Aharonov-Bohm effect
The possibility of detecting noncommutative space relics is analyzed using
the Aharonov-Bohm effect. We show that, if space is noncommutative, the
holonomy receives non-trivial kinematical corrections that will produce a
diffraction pattern even when the magnetic flux is quantized. The scattering
problem is also formulated, and the differential cross section is calculated.
Our results can be extrapolated to high energy physics and the bound is found. If this bound holds, then noncommutative
effects could be explored in scattering experiments measuring differential
cross sections for small angles. The bound state Aharonov- Bohm effect is also
discussed.Comment: 16 pp, Revtex 4, 2 fig, new references added. To appear in PR
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