Comment on `Supersymmetry, PT-symmetry and spectral bifurcation'

We demonstrate that the recent paper by Abhinav and Panigrahi entitled `Supersymmetry, PT-symmetry and spectral bifurcation' [Ann.\ Phys.\ 325 (2010) 1198], which considers two different types of superpotentials for the PT-symmetric complexified Scarf II potential, fails to take into account the invariance under the exchange of its coupling parameters. As a result, they miss the important point that for unbroken PT-symmetry this potential indeed has two series of real energy eigenvalues, to which one can associate two different superpotentials. This fact was first pointed out by the present authors during the study of complex potentials having a complex $sl(2)$ potential algebra.Comment: 6 pages, no figure, published versio

Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework

We show that complex Lie algebras (in particular sl(2,C)) provide us with an elegant method for studying the transition from real to complex eigenvalues of a class of non-Hermitian Hamiltonians: complexified Scarf II, generalized P\"oschl-Teller, and Morse. The characterizations of these Hamiltonians under the so-called pseudo-Hermiticity are also discussed.Comment: LaTeX, 14 pages, no figure, 1 reference adde

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

Identification of a hereditary system with distributed delay

We study the identification problem that arises in a linear hereditary system with distributed delay. This involves estimating an infinite-dimensional parameter and we use the method of sieves, proposed by Grenander, to solve this problem

Orbital Parameters of Binary Radio Pulsars : Revealing Their Structure, Formation, Evolution and Dynamic History

Orbital parameters of binary radio pulsars reveal the history of the pulsars' formation and evolution including dynamic interactions with other objects. Advanced technology has enabled us to determine these orbital parameters accurately in most of the cases. Determination of post-Keplerian parameters of double neutron star binaries (especially of the double pulsar) provide clean tests of GTR and in the future may lead us to constrain the dense matter EoS. For binary pulsars with MS or WD companions, knowledge about the values of the orbital parameters as well as of the spin periods and the masses of the pulsars and the companions might be useful to understand the evolutionary history of the systems. As accreting neutron star binaries lead to orbit circularization due to the tidal coupling during accretion, their descendants i.e. binary MSPs are expected to be in circular orbits. On the other hand, dense stellar environments inside globular clusters (GCs) cause different types of interactions of single stars with pulsar binaries. These interactions can impart high eccentricities to the pulsar binaries. So it is quite common to get eccentric millisecond pulsar binaries in GCs and we find that "fly-by" causes intermediate values of eccentricities while "exchange" or "merger" causes high values of eccentricities. We also show that "ionization" is not much effective in the present stage of GCs. Even in the absence of such kinds of stellar interactions, a millisecond pulsar can have an eccentric orbit as a result of Kozai resonance if the pulsar binary is a member of a hierarchical triple system. PSR J1903+0327 is the only one eccentric millisecond pulsar binary in the galactic disk where stellar interactions are negligible. The possibility of this system to be a member of a hierarchical triple system or past association of a GC have been studied and found to be less likely.Comment: Invited chapter in "Pulsars: Theory, Categories and Applications", Editor: Alexander D. Morozov, 2010, Nova Science Publishers, ISBN: 978-1-61668-919-3; Typos correcte