7,062 research outputs found
Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives
We generalise the construction of fuzzy CP^N in a manner that allows us to
access all noncommutative equivariant complex vector bundles over this space.
We give a simplified construction of polarization tensors on S^2 that
generalizes to complex projective space, identify Laplacians and natural
noncommutative covariant derivative operators that map between the modules that
describe noncommuative sections. In the process we find a natural
generalization of the Schwinger-Jordan construction to su(n) and identify
composite oscillators that obey a Heisenberg algebra on an appropriate Fock
space.Comment: 34 pages, v2 contains minor corrections to the published versio
The Information Geometry of the Ising Model on Planar Random Graphs
It has been suggested that an information geometric view of statistical
mechanics in which a metric is introduced onto the space of parameters provides
an interesting alternative characterisation of the phase structure,
particularly in the case where there are two such parameters -- such as the
Ising model with inverse temperature and external field .
In various two parameter calculable models the scalar curvature of
the information metric has been found to diverge at the phase transition point
and a plausible scaling relation postulated: . For spin models the necessity of calculating in
non-zero field has limited analytic consideration to 1D, mean-field and Bethe
lattice Ising models. In this letter we use the solution in field of the Ising
model on an ensemble of planar random graphs (where ) to evaluate the scaling behaviour of the scalar curvature, and find
. The apparent discrepancy is traced
back to the effect of a negative .Comment: Version accepted for publication in PRE, revtex
The Information Geometry of the One-Dimensional Potts Model
In various statistical-mechanical models the introduction of a metric onto
the space of parameters (e.g. the temperature variable, , and the
external field variable, , in the case of spin models) gives an alternative
perspective on the phase structure. For the one-dimensional Ising model the
scalar curvature, , of this metric can be calculated explicitly in
the thermodynamic limit and is found to be . This is positive definite and, for
physical fields and temperatures, diverges only at the zero-temperature,
zero-field ``critical point'' of the model.
In this note we calculate for the one-dimensional -state Potts
model, finding an expression of the form , where is the Potts
analogue of . This is no longer positive
definite, but once again it diverges only at the critical point in the space of
real parameters. We remark, however, that a naive analytic continuation to
complex field reveals a further divergence in the Ising and Potts curvatures at
the Lee-Yang edge.Comment: 9 pages + 4 eps figure
FIELD TESTS FOR MEDICAGO RESISTANCE AGAINST THE POTATO LEAFHOPPER (HOMOPTERA: CICADELLIDAE)
A collection of 70 Medicago introductions were field tested for resistance against potato leafhopper, Empoasca fabae (Harris), damage. All M. sativa L. ssp. sativa and most ssp. mixtures were susceptible. All ssp. falcata (L.) Arcangeli, one ssp. mixture sativa and caerulea (Lessing ex Ledebour) Schmalhausen, ssp. × varia (Martyn) Arcangeli and M. pironae Vis were resistant receiving one-half or less damage than the standard cultivars during four seasons of testing. Resistant introductions were slower in regrowth, attained less height, had smaller leaflets, thinner, tougher stems, and more prostrate growth than standard cultivars. Results suggest most observed resistance is due to avoidance of tough stems for ovipositio
Functional dissociation of amygdala-modulated arousal and cognitive appraisal, in Turner syndrome
On the Role of Chaos in the AdS/CFT Connection
The question of how infalling matter in a pure state forms a Schwarzschild
black hole that appears to be at non-zero temperature is discussed in the
context of the AdS/CFT connection. It is argued that the phenomenon of
self-thermalization in non-linear (chaotic) systems can be invoked to explain
how the boundary theory, initially at zero temperature self thermalizes and
acquires a finite temperature. Yang-Mills theory is known to be chaotic
(classically) and the imaginary part of the gluon self-energy (damping rate of
the gluon plasma) is expected to give the Lyapunov exponent. We explain how the
imaginary part would arise in the corresponding supergravity calculation due to
absorption at the horizon of the black hole.Comment: 18 pages. Latex file. Minor changes. Final version to appear in
Modern Physics Letters
Duality, the Semi-Circle Law and Quantum Hall Bilayers
There is considerable experimental evidence for the existence in Quantum Hall
systems of an approximate emergent discrete symmetry, . The evidence consists of the robustness of the tests of a suite a
predictions concerning the transitions between the phases of the system as
magnetic fields and temperatures are varied, which follow from the existence of
the symmetry alone. These include the universality of and quantum numbers of
the fixed points which occur in these transitions; selection rules governing
which phases may be related by transitions; and the semi-circular trajectories
in the Ohmic-Hall conductivity plane which are followed during the transitions.
We explore the implications of this symmetry for Quantum Hall systems involving
{\it two} charge-carrying fluids, and so obtain predictions both for bilayer
systems and for single-layer systems for which the Landau levels have a spin
degeneracy. We obtain similarly striking predictions which include the novel
new phases which are seen in these systems, as well as a prediction for
semicircle trajectories which are traversed by specific combinations of the
bilayer conductivities as magnetic fields are varied at low temperatures.Comment: 12 pages, 8 figures; discussion of magnetic field dependence modified
and figures and references updated in v
A projective Dirac operator on CP^2 within fuzzy geometry
We propose an ansatz for the commutative canonical spin_c Dirac operator on
CP^2 in a global geometric approach using the right invariant (left action-)
induced vector fields from SU(3). This ansatz is suitable for noncommutative
generalisation within the framework of fuzzy geometry. Along the way we
identify the physical spinors and construct the canonical spin_c bundle in this
formulation. The chirality operator is also given in two equivalent forms.
Finally, using representation theory we obtain the eigenspinors and calculate
the full spectrum. We use an argument from the fuzzy complex projective space
CP^2_F based on the fuzzy analogue of the unprojected spin_c bundle to show
that our commutative projected spin_c bundle has the correct
SU(3)-representation content.Comment: reduced to 27 pages, minor corrections, minor improvements, typos
correcte
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