On Exactness Of The Supersymmetric WKB Approximation Scheme

Exactness of the lowest order supersymmetric WKB (SWKB) quantization condition $\int^{x_2}_{x_1} \sqrt{E-\omega^2(x)} dx = n \hbar \pi$, for certain potentials, is examined, using complex integration technique. Comparison of the above scheme with a similar, but {\it exact} quantization condition, $\oint_c p(x,E) dx = 2\pi n \hbar$, originating from the quantum Hamilton-Jacobi formalism reveals that, the locations and the residues of the poles that contribute to these integrals match identically, for both of these cases. As these poles completely determine the eigenvalues in these two cases, the exactness of the SWKB for these potentials is accounted for. Three non-exact cases are also analysed; the origin of this non-exactness is shown to be due the presence of additional singularities in $\sqrt{E-\omega^2(x)}$, like branch cuts in the $x-$plane.Comment: 11 pages, latex, 1 figure available on reques

Accuracy of Semiclassical Methods for Shape Invariant Potentials

We study the accuracy of several alternative semiclassical methods by computing analytically the energy levels for many large classes of exactly solvable shape invariant potentials. For these potentials, the ground state energies computed via the WKB method typically deviate from the exact results by about 10%, a recently suggested modification using nonintegral Maslov indices is substantially better, and the supersymmetric WKB quantization method gives exact answers for all energy levels.Comment: 7 pages, Latex, and two tables in postscrip

Quantum interference within the complex quantum Hamilton-Jacobi formalism

Quantum interference is investigated within the complex quantum Hamilton-Jacobi formalism. As shown in a previous work [Phys. Rev. Lett. 102, 250401 (2009)], complex quantum trajectories display helical wrapping around stagnation tubes and hyperbolic deflection near vortical tubes, these structures being prominent features of quantum caves in space-time Argand plots. Here, we further analyze the divergence and vorticity of the quantum momentum function along streamlines near poles, showing the intricacy of the complex dynamics. Nevertheless, despite this behavior, we show that the appearance of the well-known interference features (on the real axis) can be easily understood in terms of the rotation of the nodal line in the complex plane. This offers a unified description of interference as well as an elegant and practical method to compute the lifetime for interference features, defined in terms of the average wrapping time, i.e., considering such features as a resonant process.Comment: revised version, 13 pages, 11 figures, 1 tabl

Calculation of Band Edge Eigenfunctions and Eigenvalues of Periodic Potentials through the Quantum Hamilton - Jacobi Formalism

We obtain the band edge eigenfunctions and the eigenvalues of solvable periodic potentials using the quantum Hamilton - Jacobi formalism. The potentials studied here are the Lam{\'e} and the associated Lam{\'e} which belong to the class of elliptic potentials. The formalism requires an assumption about the singularity structure of the quantum momentum function $p$, which satisfies the Riccati type quantum Hamilton - Jacobi equation, $p^{2} -i \hbar \frac{d}{dx}p = 2m(E- V(x))$ in the complex $x$ plane. Essential use is made of suitable conformal transformations, which leads to the eigenvalues and the eigenfunctions corresponding to the band edges in a simple and straightforward manner. Our study reveals interesting features about the singularity structure of $p$, responsible in yielding the band edge eigenfunctions and eigenvalues.Comment: 21 pages, 5 table

Knowledge-based biomedical word sense disambiguation: comparison of approaches

<p>Abstract</p> <p>Background</p> <p>Word sense disambiguation (WSD) algorithms attempt to select the proper sense of ambiguous terms in text. Resources like the UMLS provide a reference thesaurus to be used to annotate the biomedical literature. Statistical learning approaches have produced good results, but the size of the UMLS makes the production of training data infeasible to cover all the domain.</p> <p>Methods</p> <p>We present research on existing WSD approaches based on knowledge bases, which complement the studies performed on statistical learning. We compare four approaches which rely on the UMLS Metathesaurus as the source of knowledge. The first approach compares the overlap of the context of the ambiguous word to the candidate senses based on a representation built out of the definitions, synonyms and related terms. The second approach collects training data for each of the candidate senses to perform WSD based on queries built using monosemous synonyms and related terms. These queries are used to retrieve MEDLINE citations. Then, a machine learning approach is trained on this corpus. The third approach is a graph-based method which exploits the structure of the Metathesaurus network of relations to perform unsupervised WSD. This approach ranks nodes in the graph according to their relative structural importance. The last approach uses the semantic types assigned to the concepts in the Metathesaurus to perform WSD. The context of the ambiguous word and semantic types of the candidate concepts are mapped to Journal Descriptors. These mappings are compared to decide among the candidate concepts. Results are provided estimating accuracy of the different methods on the WSD test collection available from the NLM.</p> <p>Conclusions</p> <p>We have found that the last approach achieves better results compared to the other methods. The graph-based approach, using the structure of the Metathesaurus network to estimate the relevance of the Metathesaurus concepts, does not perform well compared to the first two methods. In addition, the combination of methods improves the performance over the individual approaches. On the other hand, the performance is still below statistical learning trained on manually produced data and below the maximum frequency sense baseline. Finally, we propose several directions to improve the existing methods and to improve the Metathesaurus to be more effective in WSD.</p

Measurement of the Neutron Radius of 208Pb Through Parity-Violation in Electron Scattering

We report the first measurement of the parity-violating asymmetry A_PV in the elastic scattering of polarized electrons from 208Pb. A_PV is sensitive to the radius of the neutron distribution (Rn). The result A_PV = 0.656 \pm 0.060 (stat) \pm 0.014 (syst) ppm corresponds to a difference between the radii of the neutron and proton distributions Rn - Rp = 0.33 +0.16 -0.18 fm and provides the first electroweak observation of the neutron skin which is expected in a heavy, neutron-rich nucleus.Comment: 6 pages, 1 figur