Truncated Harmonic Osillator and Parasupersymmetric Quantum Mechanics

We discuss in detail the parasupersymmetric quantum mechanics of arbitrary order where the parasupersymmetry is between the normal bosons and those corresponding to the truncated harmonic oscillator. We show that even though the parasusy algebra is different from that of the usual parasusy quantum mechanics, still the consequences of the two are identical. We further show that the parasupersymmetric quantum mechanics of arbitrary order p can also be rewritten in terms of p supercharges (i.e. all of which obey $Q_i^{2} = 0$). However, the Hamiltonian cannot be expressed in a simple form in terms of the p supercharges except in a special case. A model of conformal parasupersymmetry is also discussed and it is shown that in this case, the p supercharges, the p conformal supercharges along with Hamiltonian H, conformal generator K and dilatation generator D form a closed algebra.Comment: 9 page

Isospectral Potentials from Modified Factorization

Factorization of quantum mechanical potentials has a long history extending back to the earliest days of the subject. In the present paper, the non-uniqueness of the factorization is exploited to derive new isospectral non-singular potentials. Many one-parameter families of potentials can be generated from known potentials using a factorization that involves superpotentials defined in terms of excited states of a potential. For these cases an operator representation is available. If ladder operators are known for the original potential, then a straightforward procedure exists for defining such operators for its isospectral partners. The generality of the method is illustrated with a number of examples which may have many possible applications in atomic and molecular physics.Comment: 8 pages, 4 figure

Orientational relaxation in a discotic liquid crystal

We investigate orientational relaxation of a model discotic liquid crystal, consists of disc-like molecules, by molecular dynamics simulations along two isobars starting from the high temperature isotropic phase. The two isobars have been so chosen that (A) the phase sequence isotropic (I)-nematic (N)-columnar (C) appears upon cooling along one of them and (B) the sequence isotropic (I)-columnar (C) along the other. While the orientational relaxation in the isotropic phase near the I-N phase transition in system (A) shows a power law decay at short to intermediate times, such power law relaxation is not observed in the isotropic phase near the I-C phase boundary in system (B). In order to understand this difference (the existence or the absence of the power law decay), we calculated the the growth of the orientational pair distribution functions (OPDF) near the I-N phase boundary and also near the I-C phase boundary. We find that OPDF shows a marked growth in long range correlation as the I-N phase boundary is approached in the I-N-C system (A), but such a growth is absent in the I-C system, which appears to be consistent with the result that I-N phase transition in the former is weakly first order while the the I-C phase transition in the later is not weak. As the system settles into the nematic phase, the decay of the single-particle second-rank orientational OTCF follows a pattern that is similar to what is observed with calamitic liquid crystals and supercooled molecular liquids.Comment: 16 pages and 4 figure

Indian Coals for Sponge Iron Process

IN CONTRAST to conventional two stage process of steel making via blast furnace, direct steel making with pre-reduced iron ores or agglomerates have attracted attent-ion in recent times.This is particularly so for devolop-ing countries where there is availability of other raw materials for iron making but there is dearth of or limited resources of coking coal and abundant supply of other type of non coking coals. In terms of energy equi-valent, availability of . solid fuel is many hundred times more than that of natural gas. Extensive attempts have therefore been made to utilise non coking coals to produce iron by non conventional methods such as direct reduction processes. The solid iron produced by reduction technique known as 'sponge' can then be trans-formed into steel by melting. An attempt has been made in the paper to indicate the available resources of Indian coals, their nature and property which may be considered suitable for the prod-uction of sponge i ron either as such or after benef-iciation. Indications have also been given for the possi-bility of utilising char from the fluid bed carbonisation of non coking coal where such material can be obtained from an integrated formed coke plant

High-Dimensional Topological Insulators with Quaternionic Analytic Landau Levels

We study the 3D topological insulators in the continuum by coupling spin-1/2 fermions to the Aharonov-Casher SU(2) gauge field. They exhibit flat Landau levels in which orbital angular momentum and spin are coupled with a fixed helicity. The 3D lowest Landau level wavefunctions exhibit the quaternionic analyticity as a generalization of the complex analyticity of the 2D case. Each Landau level contributes one branch of gapless helical Dirac modes to the surface spectra, whose topological properties belong to the Z2-class. The flat Landau levels can be generalized to an arbitrary dimension. Interaction effects and experimental realizations are also studied

Entropy of three-dimensional asymptotically flat cosmological solutions

The thermodynamics of three-dimensional asymptotically flat cosmological solutions that play the same role than the BTZ black holes in the anti-de Sitter case is derived and explained from holographic properties of flat space. It is shown to coincide with the flat-space limit of the thermodynamics of the inner black hole horizon on the one hand and the semi-classical approximation to the gravitational partition function associated to the entropy of the outer horizon on the other. This leads to the insight that it is the Massieu function that is universal in the sense that it can be computed at either horizon.Comment: 16 pages Latex file, v2: references added, cosmetic changes, v3: 1 reference adde

Quantum Hamilton-Jacobi analysis of PT symmetric Hamiltonians

We apply the quantum Hamilton-Jacobi formalism, naturally defined in the complex domain, to a number of complex Hamiltonians, characterized by discrete parity and time reversal (PT) symmetries and obtain their eigenvalues and eigenfunctions. Examples of both quasi-exactly and exactly solvable potentials are analyzed and the subtle differences, in the singularity structures of their quantum momentum functions, are pointed out. The role of the PT symmetry in the complex domain is also illustrated.Comment: 11 page

Spectral and polarization study of the double relics in Abell 3376 using the GMRT and the VLA

Double radio relics in galaxy clusters are rare phenomena that trace shocks in the outskirts of merging galaxy clusters. We have carried out a spectral and polarization study of the spectacular double relics in the galaxy cluster A3376 using the Giant Metrewave Radio Telescope at 150 and 325 MHz and the Very Large Array at 1400 MHz. The polarization study at 1400 MHz reveals a high degree of polarization (~30%) and aligned magnetic field vectors (not corrected for Faraday rotation) in the eastern relic. A highly polarized (>60%) filamentary radio source of size ~300 kpc near the eastern relic and north of the bent-jet radio galaxy is detected for the first time. The western relic is less polarized and does not show aligned magnetic field vectors. The distribution of spectral indices between 325 and 1400 MHz over the radio relics show steepening from the outer to the inner edges of the relics. The spectral indices of the eastern and the western relics imply Mach numbers in the range 2.2 to 3.3. Remarkable features such as the inward filament extending from the eastern relic, the highly polarized filament, the complex polarization properties of the western relic and the separation of the BCG from the ICM by a distance >900 kpc are noticed in the cluster. A comparison with simulated cluster mergers is required to understand the complex properties of the double relics in the context of the merger in A3376. An upper limit (log(P(1.4GHz) W/Hz < 23.0) on the strength of a Mpc size radio halo in A3376 is estimated.Comment: 9 pages, 4 figures, accepted for publication in MNRA