Shape Invariant Rational Extensions And Potentials Related to Exceptional Polynomials

In this paper, we show that an attempt to construct shape invariant extensions of a known shape invariant potential leads to, apart from a shift by a constant, the well known technique of isospectral shift deformation. Using this, we construct infinite sets of generalized potentials with $X_m$ exceptional polynomials as solutions. These potentials are rational extensions of the existing shape invariant potentials. The method is elucidated using the radial oscillator and the trigonometric P\"{o}schl-Teller potentials. For the case of radial oscillator, in addition to the known rational extensions, we construct two infinite sets of rational extensions, which seem to be less studied. For one of the potential, we show that its solutions involve a third type of exceptional Laguerre polynomials. Explicit expressions of this generalized infinite set of potentials and the corresponding solutions are presented. For the trigonometric P\"{o}schl-Teller potential, our analysis points to the possibility of several rational extensions beyond those known in literature.Comment: 18 pages, 1 figur

MMT Survey for Intervening MgII Absorption

We present the results from a spectroscopic survey for intervening MgII absorption in the spectra of 381 background QSOs conducted at the Multiple Mirror Telescope. This survey complements our earlier SDSS EDR MgII survey, extending our results to lower redshift ($z \simeq 0.15$) and weaker MgII $\lambda2796$ rest equivalent width ($W_0^{\lambda2796} \simeq 0.1$\AA). We confirm two major results from that survey: the transition in the $W_0^{\lambda2796}$ distribution at $W_0^{\lambda2796} \approx 0.3$\AA, and the $W_0^{\lambda2796}$-dependent evolution of the incidence of systems. The nature of $\partial^2N/\partial z \partial W_0^{\lambda2796}$ is consistent with the idea that multiple physically-distinct components/processes contribute to the incidence of MgII absorption systems in a $W_0$-dependent manner and evolve at different rates. A significant decrease in the total proper absorption cross section is detected in our MMT data for systems as weak as 1.0 \AA $\le W_0^{\lambda2796} < 1.5$\AA at $z\lesssim 0.4$. We discuss this $W_0$-dependent evolution in the context of the evolution of galaxy structures, processes including superwinds and interactions, and damped-Ly$\alpha$ absorbers. We also consider the possibility that the observed redshift and $W_0^{\lambda2796}$ dependence of the incidence of absorption in spectroscopic surveys for low-ion/neutral gas results from the effects of dust-induced extinction.Comment: 16 pages, 7 figures, accepted for publication in The Astrophysical Journa

Magnetic interactions in the Martensitic phase of Mn rich Ni-Mn-In shape memory alloys

The magnetic properties of Mn$_{2}$Ni$_{(1+x)}$In$_{(1-x)}$ ($x$ = 0.5, 0.6, 0.7) and Mn$_{(2-y)}$Ni$_{(1.6+y)}$In$_{0.4}$ ($y$ = -0.08, -0.04, 0.04, 0.08) shape memory alloys have been studied. Magnetic interactions in the martensitic phase of these alloys are found to be quite similar to those in Ni$_2$Mn$_{(1+x)}$In$_{(1-x)}$ type alloys. Doping of Ni for In not only induces martensitic instability in Mn$_2$NiIn type alloys but also affects magnetic properties due to a site occupancy disorder. Excess Ni preferentially occupies X sites forcing Mn to the Z sites of X$_2$YZ Heusler composition resulting in a transition from ferromagnetic ground state to a state dominated by ferromagnetic Mn(Y) - Mn(Y) and antiferromagnetic Mn(Y)-Mn(Z) interactions. These changes in magnetic ground state manifest themselves in observation of exchange bias effect even in zero field cooled condition and virgin magnetization curve lying outside the hysteresis loop.Comment: Accepted in J. Appl. Phy

Ca II Absorbers in the Sloan Digital Sky Survey: Statistics

We present the results of a survey for CaII 3934,3969 absorption-line systems culled from ~ 95,000 Sloan Digital Sky Survey (SDSS) Data Release 7 and Data Release 9 quasar spectra. With 435 doublets identified in the catalog, this list is the largest CaII catalog compiled to date, spanning redshifts z < 1.34, which corresponds to the most recent ~ 8.9 Gyrs of the history of the Universe. We derive statistics on the CaII rest equivalent width distribution (REW) and incidence (number density per unit redshift). We find that the lambda3934 REW distribution cannot be described by a single exponential function. A double exponential function is required to produce a satisfactory description. The function can be written as a sum of weak and strong components: dn/dW = (N_wk*/W_wk*) exp(-W/W_wk*) + (N_str*/W_str*) exp(-W/W_str*). A maximum likelihood fit to the unbinned data indicates: N_wk*=0.140 +/- 0.029, W_wk*=0.165 +/- 0.020 A, N_str*=0.024 +/- 0.020, and W_str*=0.427 +/- 0.101 A. This suggests that the CaII absorbers are composed of at least two distinct populations. The incidence (product of integrated absorber cross section and their co-moving number density) of the overall CaII absorber population does not show evidence for evolution in the standard cosmology. The normalization of the no-evolution curve, i.e., the value of the CaII incidence extrapolated to redshift z=0, for lambda 3934 >= 0.3 A, is n_0=0.017 +/- 0.001. In comparison to MgII surveys, we found that only 3% of MgII systems in the SDSS have CaII, confirming that it is rare to identify CaII in quasar absorption-line surveys. We also report on some preliminary investigations of the nature of the two populations of CaII absorbers, and show that they can likely be distinguished using their MgII properties.Comment: Submitted to MNRA

Lepton Masses in a Minimal Model with Triplet Higgs Bosons and S3S_3 Flavor Symmetry

Viable neutrino and charged lepton masses and mixings are obtained by imposing a $S_3 \times Z_4 \times Z_3$ flavor symmetry in a model with a few additional Higgs. We use two $SU(2)_L$ triplet Higgs which are arranged as a doublet of $S_3$, and standard model singlet Higgs which are also put as doublets of $S_3$. We break the $S_3$ symmetry in this minimal model by giving vacuum expectation values (VEV) to the additional Higgs fields. Dictated by the minimum condition for the scalar potential, we obtain certain VEV alignments which allow us to maintain $\mu-\tau$ symmetry in the neutrino sector, while breaking it maximally for the charged leptons. This helps us to simultaneously explain the hierarchical charged lepton masses, and the neutrino masses and mixings. In particular, we obtain maximal $\theta_{23}$ and zero $\theta_{13}$. We allow for a mild breaking of the $\mu-\tau$ symmetry for the neutrinos and study the phenomenology. We give predictions for $\theta_{13}$ and the CP violating Jarlskog invariant $J_{CP}$, as a function of the $\mu-\tau$ symmetry breaking parameter. We also discuss possible collider signatures and phenomenology associated with lepton flavor violating processes.Comment: 29 pages, 5 figures. Version to be appeared in PRD. Phenomenology of Lepton flavor violation and possible collider signatures of this model have been include