Supersymmetry Across Nanoscale Heterojunction

We argue that supersymmetric transformation could be applied across the heterojunction formed by joining of two mixed semiconductors. A general framework is described by specifying the structure of ladder operators at the junction for making quantitative estimation of physical quantities. For a particular heterojunction device, we show that an exponential grading inside a nanoscale doped layer is amenable to exact analytical treatment for a class of potentials distorted by the junctions through the solutions of transformed Morse-Type potentials.Comment: 7 pages, 2 figure

New classes of quasi-solvable potentials, their exactly-solvable limit and related orthogonal polynomials

We have generated, using an sl(2,R) formalism, several new classes of quasi-solvable elliptic potentials, which in the appropriate limit go over to the exactly solvable forms. We have obtained exact solutions of the corresponding spectral problems for some real values of the potential parameters. We have also given explicit expressions of the families of associated orthogonal polynomials in the energy variable.Comment: 14 pages, 5 tables, LaTeX2

Soliton Lattice and Single Soliton Solutions of the Associated Lam\'e and Lam\'e Potentials

We obtain the exact nontopological soliton lattice solutions of the Associated Lam\'e equation in different parameter regimes and compute the corresponding energy for each of these solutions. We show that in specific limits these solutions give rise to nontopological (pulse-like) single solitons, as well as to different types of topological (kink-like) single soliton solutions of the Associated Lam\'e equation. Following Manton, we also compute, as an illustration, the asymptotic interaction energy between these soliton solutions in one particular case. Finally, in specific limits, we deduce the soliton lattices, as well as the topological single soliton solutions of the Lam\'e equation, and also the sine-Gordon soliton solution.Comment: 23 pages, 5 figures. Submitted to J. Math. Phy

The Absorbers Toward CSO 118: Superclustering at {z~3}, or an Intrinsic Absorption Complex?

We present two low resolution (R~1300) high signal-to-noise spectra (Wr,lim~50mA) of the quasar CSO 118 (zem=2.97) taken with the Hobby-Eberly Telescope Marcario Low Resolution Spectrograph. We detect eight absorbers selected by the CIV 1548,1550 absorption doublet in the redshift range {2.23 < zabs 2.68. In the redshift range covered by the seven zabs > 2.68 systems, one expects to find two absorbers. We discuss possible explanations for such an excess of absorbers in a small velocity range. Only superclustering at high redshift and absorption due to intrinsic gas are feasibly allowed.Comment: 12 pages total, 2 tables, 2 figures, accepted for publication in ApJ Letter

Associated Lam\'{E} Equation, Periodic Potentials and sl(2,R)

We propose a new approach based on the algebraization of the Associated Lam\'{e} equation $$-\psi''(x) + [ m(m+1)k^{2}sn^{2}x + \ell(\ell+1)k^{2}(cn^{2}x/dn^{2}x)]\psi(x) = E\psi(x)$$ within sl(2,R) to derive the corresponding periodic potentials. The band edge eigenfunctions and energy spectra are explicitly obtained for integers m,$\ell$. We also obtain the explicit expressions of the solutions for half-integer m and integer or half-integer $\ell$.Comment: 8 pages, no figure, tex file(version 2.09