4,750 research outputs found
Non-commutative Complex Projective Spaces and the Standard Model
The standard model fermion spectrum, including a right handed neutrino, can
be obtained as a zero-mode of the Dirac operator on a space which is the
product of complex projective spaces of complex dimension two and three. The
construction requires the introduction of topologically non-trivial background
gauge fields. By borrowing from ideas in Connes' non-commutative geometry and
making the complex spaces `fuzzy' a matrix approximation to the fuzzy space
allows for three generations to emerge. The generations are associated with
three copies of space-time. Higgs' fields and Yukawa couplings can be
accommodated in the usual way.Comment: Contribution to conference in honour of A.P. Balachandran's 65th
birthday: "Space-time and Fundamental Interactions: Quantum Aspects", Vietri
sul Mare, Italy, 25th-31st May, 2003, 10 pages, typset in LaTe
The Quantum Hall Effect in Graphene: Emergent Modular Symmetry and the Semi-circle Law
Low-energy transport measurements in Quantum Hall systems have been argued to
be governed by emergent modular symmetries whose predictions are robust against
many of the detailed microscopic dynamics. We propose the recently-observed
quantum Hall effect in graphene as a test of these ideas, and identify to this
end a class of predictions for graphene which would follow from the same
modular arguments. We are led to a suite of predictions for high mobility
samples that differs from those obtained for the conventional quantum Hall
effect in semiconductors, including: predictions for the locations of the
quantum Hall plateaux; predictions for the positions of critical points on
transitions between plateaux; a selection rule for which plateaux can be
connected by low-temperature transitions; and a semi-circle law for
conductivities traversed during these transitions. Many of these predictions
appear to provide a good description of graphene measurements performed with
intermediate-strength magnetic fields.Comment: 4 pages, 2 figure
Compressibility of rotating black holes
Interpreting the cosmological constant as a pressure, whose thermodynamically
conjugate variable is a volume, modifies the first law of black hole
thermodynamics. Properties of the resulting thermodynamic volume are
investigated: the compressibility and the speed of sound of the black hole are
derived in the case of non-positive cosmological constant. The adiabatic
compressibility vanishes for a non-rotating black hole and is maximal in the
extremal case --- comparable with, but still less than, that of a cold neutron
star. A speed of sound is associated with the adiabatic compressibility,
which is is equal to for a non-rotating black hole and decreases as the
angular momentum is increased. An extremal black hole has
when the cosmological constant vanishes, and more generally is bounded
below by .Comment: 8 pages, 1 figure, uses revtex4, references added in v
Noncommutative BTZ Black Hole and Discrete Time
We search for all Poisson brackets for the BTZ black hole which are
consistent with the geometry of the commutative solution and are of lowest
order in the embedding coordinates. For arbitrary values for the angular
momentum we obtain two two-parameter families of contact structures. We obtain
the symplectic leaves, which characterize the irreducible representations of
the noncommutative theory. The requirement that they be invariant under the
action of the isometry group restricts to symplectic leaves,
where is associated with the Schwarzschild time. Quantization may then lead
to a discrete spectrum for the time operator.Comment: 10 page
Recommended from our members
Learning Contextual Reward Expectations for Value Adaptation
Substantial evidence indicates that subjective value is adapted to the statistics of reward expected within a given temporal context. However, how these contextual expectations are learned is poorly understood. To examine such learning, we exploited a recent observation that participants performing a gambling task adjust their preferences as a function of context. We show that, in the absence of contextual cues providing reward information, an average reward expectation was learned from recent past experience. Learning dependent on contextual cues emerged when two contexts alternated at a fast rate, whereas both cue-independent and cue-dependent forms of learning were apparent when two contexts alternated at a slower rate. Motivated by these behavioral findings, we reanalyzed a previous fMRI data set to probe the neural substrates of learning contextual reward expectations. We observed a form of reward prediction error related to average reward such that, at option presentation, activity in ventral tegmental area/substantia nigra and ventral striatum correlated positively and negatively, respectively, with the actual and predicted value of options. Moreover, an inverse correlation between activity in ventral tegmental area/substantia nigra (but not striatum) and predicted option value was greater in participants showing enhanced choice adaptation to context. The findings help understanding the mechanisms underlying learning of contextual reward expectation
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
Shoreline configuration and shoreline dynamics: A mesoscale analysis
The author has identified the following significant results. Atlantic coast barrier island shorelines are seldom straight, but rather sinuous. These shoreline curvatures range in size from cusps to capes. Significant relationships exist between the orientation of shoreline segments within the larger of these sinuous features and shoreline dynamics, with coefficients ranging up to .9. Orientation of the shoreline segments of Assateague Island (60 km) and the Outer Banks of North Carolina (130 km) was measured from LANDSAT 2 imagery (1:80,000) and high altitude aerial photography (1:120,000). Long term trends in shoreline dynamics were established by mapping shoreline and storm-surge penetration changes
LANDSAT application of remote sensing to shoreline-form analysis
The author has identified the following significant results. Orientation of the shoreline segments of Assateague Island (55 km) was measured from LANDSAT 2 imagery enlarged to 1:250,000 and 1:80,000. Long term trends in shoreline dynamics were established by mapping shoreline and storm-surge penetration changes from historical low altitude aerial photography spanning four decades
Isolated critical point from Lovelock gravity
For any K(=2k+1)th-order Lovelock gravity with fine-tuned Lovelock couplings,
we demonstrate the existence of a special isolated critical point characterized
by non-standard critical exponents in the phase diagram of hyperbolic vacuum
black holes. In the Gibbs free energy this corresponds to a place wherefrom two
swallowtails emerge, giving rise to two first-order phase transitions between
small and large black holes. We believe that this is a first example of a
critical point with non-standard critical exponents obtained in a geometric
theory of gravity.Comment: 5 pages, 2 figure
On the "Universal" Quantum Area Spectrum
There has been much debate over the form of the quantum area spectrum for a
black hole horizon, with the evenly spaced conception of Bekenstein having
featured prominently in the discourse. In this letter, we refine a very
recently proposed method for calibrating the Bekenstein form of the spectrum.
Our refined treatment predicts, as did its predecessor, a uniform spacing
between adjacent spectral levels of in Planck units; notably, an outcome
that already has a pedigree as a proposed ``universal'' value for this
intrinsically quantum-gravitational measure. Although the two approaches are
somewhat similar in logic and quite agreeable in outcome, we argue that our
version is conceptually more elegant and formally simpler than its precursor.
Moreover, our rendition is able to circumvent a couple of previously unnoticed
technical issues and, as an added bonus, translates to generic theories of
gravity in a very direct manner.Comment: 7 Pages; (v2) now 9 full pages, significant changes to the text and
material added but the general theme and conclusions are unchange
- …