444 research outputs found
Fractional Quantum Hall Effect from Anomalies in WZNW Model
An approach to understand Fractional Quantum Hall Effect (FQHE) using
anomalies is studied in this paper. More specifically, this is done by looking
at the anomaly in the current conservation equation of a WZNW theory describing
fields living at the edge of the two dimensional Hall sample. This WZNW theory
itself comes from the non-Abelian bosonisation of fermions living at the edge.
It is shown that this model can describe both integer and fractional
quantization of conductivities in a unified manner.Comment: 14 pages, SU-4240-56
Edge States and Entanglement Entropy
It is known that gauge fields defined on manifolds with spatial boundaries
support states localized at the boundaries. In this paper, we demonstrate how
coarse-graining over these states can lead to an entanglement entropy. In
particular, we show that the entanglement entropy of the ground state for the
quantum Hall effect on a disk exhibits an approximate ``area " law.Comment: 16 pages, minor corrections and futher details adde
Edge States in Gauge Theories: Theory, Interpretations and Predictions
Gauge theories on manifolds with spatial boundaries are studied. It is shown
that observables localized at the boundaries (edge observables) can occur in
such models irrespective of the dimensionality of spacetime. The intimate
connection of these observables to charge fractionation, vertex operators and
topological field theories is described. The edge observables, however, may or
may not exist as well-defined operators in a fully quantized theory depending
on the boundary conditions imposed on the fields and their momenta. The latter
are obtained by requiring the Hamiltonian of the theory to be self-adjoint and
positive definite. We show that these boundary conditions can also have nice
physical interpretations in terms of certain experimental parameters such as
the penetration depth of the electromagnetic field in a surrounding
superconducting medium. The dependence of the spectrum on one such parameter is
explicitly exhibited for the Higgs model on a spatial disc in its London limit.
It should be possible to test such dependences experimentally, the above Higgs
model for example being a model for a superconductor. Boundary conditions for
the 3+1 dimensional system confined to a spatial ball are studied. Their
physical meaning is clarified and their influence on the edge states of this
system (known to exist under certain conditions) is discussed. It is pointed
out that edge states occur for topological solitons of gauge theories such as
the 't Hooft-Polyakov monopoles.Comment: 36 pages, LATEX File (revised because figures had problems
The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals
We have observed the production of strings (disclination lines and loops) via
the Kibble mechanism of domain (bubble) formation in the isotropic to nematic
phase transition of a sample of uniaxial nematic liquid crystal. The probablity
of string formation per bubble is measured to be . This is in
good agreement with the theoretical value expected in two dimensions
for the order parameter space of a simple uniaxial nematic
liquid crystal.Comment: 17 pages, in TEX, 2 figures (not included, available on request
The Breakdown of Linear Elastic Fracture Mechanics near the Tip of a Rapid Crack
We present high resolution measurements of the displacement and strain fields
near the tip of a dynamic (Mode I) crack. The experiments are performed on
polyacrylamide gels, brittle elastomers whose fracture dynamics mirror those of
typical brittle amorphous materials. Over a wide range of propagation
velocities (), we compare linear elastic fracture mechanics (LEFM)
to the measured near-tip fields. We find that, sufficiently near the tip, the
measured stress intensity factor appears to be non-unique, the crack tip
significantly deviates from its predicted parabolic form, and the strains ahead
of the tip are more singular than the divergence predicted by LEFM.
These results show how LEFM breaks down as the crack tip is approached.Comment: 4 pages, 4 figures, first of a two-paper series (experiments); no
change in content, minor textual revision
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