Composite Fermions and Landau Level Mixing in the Fractional Quantum Hall Effect

The reduction of the energy gap due to Landau level mixing, characterized by the dimensionless parameter $\lambda = (e^2/\epsilon l_0)/\hbar\omega_c$, has been calculated by variational Monte Carlo for the fractional quantum Hall effect at filling fractions $\nu=1/3$ and 1/5 using a modified version of Jain's composite fermion wave functions. These wave functions exploit the Landau level mixing already present in composite fermion wave functions by introducing a partial Landau level projection operator. Results for the energy gaps are consistent with experimental observations in $n$-type GaAs, but we conclude that Landau level mixing alone cannot account for the significantly smaller energy gaps observed in $p$-type systems.Comment: 11 pages, RevTex, 2 figures in compressed tar .ps forma

Unconstrained Scene Text and Video Text Recognition for Arabic Script

Building robust recognizers for Arabic has always been challenging. We demonstrate the effectiveness of an end-to-end trainable CNN-RNN hybrid architecture in recognizing Arabic text in videos and natural scenes. We outperform previous state-of-the-art on two publicly available video text datasets - ALIF and ACTIV. For the scene text recognition task, we introduce a new Arabic scene text dataset and establish baseline results. For scripts like Arabic, a major challenge in developing robust recognizers is the lack of large quantity of annotated data. We overcome this by synthesising millions of Arabic text images from a large vocabulary of Arabic words and phrases. Our implementation is built on top of the model introduced here [37] which is proven quite effective for English scene text recognition. The model follows a segmentation-free, sequence to sequence transcription approach. The network transcribes a sequence of convolutional features from the input image to a sequence of target labels. This does away with the need for segmenting input image into constituent characters/glyphs, which is often difficult for Arabic script. Further, the ability of RNNs to model contextual dependencies yields superior recognition results.Comment: 5 page

Eigenvalue spectrum for single particle in a spheroidal cavity: A Semiclassical approach

Following the semiclassical formalism of Strutinsky et al., we have obtained the complete eigenvalue spectrum for a particle enclosed in an infinitely high spheroidal cavity. Our spheroidal trace formula also reproduces the results of a spherical billiard in the limit $\eta\to1.0$. Inclusion of repetition of each family of the orbits with reference to the largest one significantly improves the eigenvalues of sphere and an exact comparison with the quantum mechanical results is observed upto the second decimal place for $kR_{0}\geq{7}$. The contributions of the equatorial, the planar (in the axis of symmetry plane) and the non-planar(3-Dimensional) orbits are obtained from the same trace formula by using the appropriate conditions. The resulting eigenvalues compare very well with the quantum mechanical eigenvalues at normal deformation. It is interesting that the partial sum of equatorial orbits leads to eigenvalues with maximum angular momentum projection, while the summing of planar orbits leads to eigenvalues with $L_z=0$ except for L=1. The remaining quantum mechanical eigenvalues are observed to arise from the 3-dimensional(3D) orbits. Very few spurious eigenvalues arise in these partial sums. This result establishes the important role of 3D orbits even at normal deformations.Comment: 17 pages, 7 ps figure

All tree level scattering amplitudes in Chern-Simons theories with fundamental matter

We show that Britto-Cachazo-Feng-Witten (BCFW) recursion relations can be used to compute all tree level scattering amplitudes in terms of $2\rightarrow2$ scattering amplitude in $U(N)$ ${\mathcal N}=2$ Chern-Simons (CS) theory coupled to matter in fundamental representation. As a byproduct, we also obtain a recursion relation for the CS theory coupled to regular fermions, even though in this case standard BCFW deformations do not have a good asymptotic behaviour. Moreover at large $N$, $2\rightarrow 2$ scattering can be computed exactly to all orders in 't Hooft coupling as was done in earlier works by some of the authors. In particular, for ${\mathcal N}=2$ theory, it was shown that $2\rightarrow 2$ scattering is tree level exact to all orders except in the anyonic channel arXiv:1505.06571, where it gets renormalized by a simple function of 't Hooft coupling. This suggests that it may be possible to compute the all loop exact result for arbitrary higher point scattering amplitudes at large $N$.Comment: RevTEX 4.1, 5 pages+6 Appendices, 7 figures; V2 Published versio

Electromagnetic Form Factors and the Localization of Quark Orbital Angular Momentum in the Proton

A new picture is given of generalized parton distributions probed in experiments in which the probe scale $Q^{2}$ and the momentum transfer \DD^{2} are well separated. Application of this picture to the $Q^{2}$ dependence of the form factors $F_{1}, F_{2}$ shows that gauge invariant quark orbital angular momentum can be measured and indeed {\it localized} in the transverse profile of the proton. A previous prediction that $\sqrt{Q^{2}}F_{2}(Q^{2})/F_{1}(Q^{2}) \sim const.$ is generalized to GPD language. This prediction appears to have been confirmed by recent CEBAF data.Comment: 6 pages, 1 figure. To appear in DIS 2001, 9th International Workshop on Deep Inelastic Scattering, Bologna, 27 April - 1 May, 200