476 research outputs found
Exponential mixing and log h time scales in quantized hyperbolic maps on the torus
We study the behaviour, in the simultaneous limits \hbar going to 0, t going
to \infty, of the Husimi and Wigner distributions of initial coherent states
and position eigenstates, evolved under the quantized hyperbolic toral
automorphisms and the quantized baker map. We show how the exponential mixing
of the underlying dynamics manifests itself in those quantities on time scales
logarithmic in \hbar. The phase space distributions of the coherent states,
evolved under either of those dynamics, are shown to equidistribute on the
torus in the limit \hbar going to 0, for times t between |\log\hbar|/(2\gamma)
and |\log|\hbar|/\gamma, where \gamma is the Lyapounov exponent of the
classical system. For times shorter than |\log\hbar|/(2\gamma), they remain
concentrated on the classical trajectory of the center of the coherent state.
The behaviour of the phase space distributions of evolved position eigenstates,
on the other hand, is not the same for the quantized automorphisms as for the
baker map. In the first case, they equidistribute provided t goes to \infty as
\hbar goes to 0, and as long as t is shorter than |\log\hbar|/\gamma. In the
second case, they remain localized on the evolved initial position at all such
times
Comparing Poisson Sigma Model with A-model
We discuss the A-model as a gauge fixing of the Poisson Sigma Model with
target a symplectic structure. We complete the discussion in [arXiv:0706.3164],
where a gauge fixing defined by a compatible complex structure was introduced,
by showing how to recover the A-model hierarchy of observables in terms of the
AKSZ observables. Moreover, we discuss the off-shell supersymmetry of the
A-model as a residual BV symmetry of the gauge-fixed PSM action.Comment: 15 pages, one missing reference adde
Geometric quantization and non-perturbative Poisson sigma model
In this note we point out the striking relation between the conditions
arising within geometric quantization and the non-perturbative Poisson sigma
model. Starting from the Poisson sigma model, we analyze necessary requirements
on the path integral measure which imply a certain integrality condition for
the Poisson cohomology class .
The same condition was considered before by Crainic and Zhu but in a
different context.
In the case when is in the image of the sharp map we reproduce the
Vaisman's condition for prequantizable Poisson manifolds. For integrable
Poisson manifolds we show, with a different procedure than in Crainic and Zhu,
that our integrality condition implies the prequantizability of the symplectic
groupoid. Using the relation between prequantization and symplectic reduction
we construct the explicit prequantum line bundle for a symplectic groupoid.
This picture supports the program of quantization of Poisson manifold via
symplectic groupoid. At the end we discuss the case of a generic coisotropic
D-brane.Comment: 29 page
Observables in the equivariant A-model
We discuss observables of an equivariant extension of the A-model in the
framework of the AKSZ construction. We introduce the A-model observables, a
class of observables that are homotopically equivalent to the canonical AKSZ
observables but are better behaved in the gauge fixing. We discuss them for two
different choices of gauge fixing: the first one is conjectured to compute the
correlators of the A-model with target the Marsden-Weinstein reduced space; in
the second one we recover the topological Yang-Mills action coupled with
A-model so that the A-model observables are closed under supersymmetry.Comment: 16 pages; minor correction
AKSZ construction from reduction data
We discuss a general procedure to encode the reduction of the target space
geometry into AKSZ sigma models. This is done by considering the AKSZ
construction with target the BFV model for constrained graded symplectic
manifolds. We investigate the relation between this sigma model and the one
with the reduced structure. We also discuss several examples in dimension two
and three when the symmetries come from Lie group actions and systematically
recover models already proposed in the literature.Comment: 42 page
Free q-Schrodinger Equation from Homogeneous Spaces of the 2-dim Euclidean Quantum Group
After a preliminary review of the definition and the general properties of
the homogeneous spaces of quantum groups, the quantum hyperboloid qH and the
quantum plane qP are determined as homogeneous spaces of Fq(E(2)). The
canonical action of Eq(2) is used to define a natural q-analog of the free
Schro"dinger equation, that is studied in the momentum and angular momentum
bases. In the first case the eigenfunctions are factorized in terms of products
of two q-exponentials. In the second case we determine the eigenstates of the
unitary representation, which, in the qP case, are given in terms of Hahn-Exton
functions. Introducing the universal T-matrix for Eq(2) we prove that the
Hahn-Exton as well as Jackson q-Bessel functions are also obtained as matrix
elements of T, thus giving the correct extension to quantum groups of well
known methods in harmonic analysis.Comment: 19 pages, plain tex, revised version with added materia
Differential calculus on the quantum Heisenberg group
The differential calculus on the quantum Heisenberg group is conlinebreak
structed. The duality between quantum Heisenberg group and algebra is proved.Comment: AMSTeX, Pages
Towards equivariant Yang-Mills theory
We study four dimensional gauge theories in the context of an equivariant
extension of the Batalin-Vilkovisky (BV) formalism. We discuss the embedding of
BV Yang-Mills (YM) theory into a larger BV theory and their relation. Partial
integration in the equivariant BV setting (BV push-forward map) is performed
explicitly for the abelian case. As result, we obtain a non-local homological
generalization of the Cartan calculus and a non-local extension of the abelian
YM BV action which satisfies the equivariant master equation.Comment: 27 pages, refs added, published versio
COCO_TS Dataset: Pixel-level Annotations Based on Weak Supervision for Scene Text Segmentation
The absence of large scale datasets with pixel-level supervisions is a
significant obstacle for the training of deep convolutional networks for scene
text segmentation. For this reason, synthetic data generation is normally
employed to enlarge the training dataset. Nonetheless, synthetic data cannot
reproduce the complexity and variability of natural images. In this paper, a
weakly supervised learning approach is used to reduce the shift between
training on real and synthetic data. Pixel-level supervisions for a text
detection dataset (i.e. where only bounding-box annotations are available) are
generated. In particular, the COCO-Text-Segmentation (COCO_TS) dataset, which
provides pixel-level supervisions for the COCO-Text dataset, is created and
released. The generated annotations are used to train a deep convolutional
neural network for semantic segmentation. Experiments show that the proposed
dataset can be used instead of synthetic data, allowing us to use only a
fraction of the training samples and significantly improving the performances
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