Spontaneous Symmetry Breaking and the Renormalization of the Chern-Simons Term

We calculate the one-loop perturbative correction to the coefficient of the \cs term in non-abelian gauge theory in the presence of Higgs fields, with a variety of symmetry-breaking structures. In the case of a residual $U(1)$ symmetry, radiative corrections do not change the coefficient of the \cs term. In the case of an unbroken non-abelian subgroup, the coefficient of the relevant \cs term (suitably normalized) attains an integral correction, as required for consistency of the quantum theory. Interestingly, this coefficient arises purely from the unbroken non-abelian sector in question; the orthogonal sector makes no contribution. This implies that the coefficient of the \cs term is a discontinuous function over the phase diagram of the theory.Comment: Version to be published in Phys Lett B., minor additional change

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

Sampling in Coal Handling and Preparation Plants

Sampling is the art of withdrawing a small quantity of material from a large lot in such a manner that the smaller fraction represents proportionally the same spec-ific composition and quality as present in the original entire lot. This is a difficult task and unless due atte-ntion is given to the sampling system white designing a plant it is not possible to achieve satisfactory results in our day to day practice. Attempt has been made in the present article to setforth some practical aspects of sampling and sampling procedure. Readers should use their own discretion and judgement to modify these techniques to suit their particular requirements always keeping in mind that the procedure adopted remained reliable and accurate

Barrier Penetration for Supersymmetric Shape-Invariant Potentials

Exact reflection and transmission coefficients for supersymmetric shape-invariant potentials barriers are calculated by an analytical continuation of the asymptotic wave functions obtained via the introduction of new generalized ladder operators. The general form of the wave function is obtained by the use of the F-matrix formalism of Froman and Froman which is related to the evolution of asymptotic wave function coefficients

Pseudo-hermitian interaction between an oscillator and a spin half particle in the external magnetic field

We consider a spin half particle in the external magnetic field which couples to a harmonic oscillator through some pseudo-hermitian interaction. We find that the energy eigenvalues for this system are real even though the interaction is not PT invariant.Comment: Latex, no figs, 8 pages. (To appear in Mod. Phys. Lett. A

PT-Symmetric, Quasi-Exactly Solvable matrix Hamiltonians

Matrix quasi exactly solvable operators are considered and new conditions are determined to test whether a matrix differential operator possesses one or several finite dimensional invariant vector spaces. New examples of $2\times 2$-matrix quasi exactly solvable operators are constructed with the emphasis set on PT-symmetric Hamiltonians.Comment: 14 pages, 1 figure, one equation corrected, results adde

Optical constants of solid methane

Methane is the most abundant simple organic molecule in the outer solar system bodies. In addition to being a gaseous constituent of the atmospheres of the Jovian planets and Titan, it is present in the solid form as a constituent of icy surfaces such as those of Triton and Pluto, and as cloud condensate in the atmospheres of Titan, Uranus, and Neptune. It is expected in the liquid form as a constituent of the ocean of Titan. Cometary ices also contain solid methane. The optical constants for both solid and liquid phases of CH4 for a wide temperature range are needed for radiative transfer calculations, for studies of reflection from surfaces, and for modeling of emission in the far infrared and microwave regions. The astronomically important visual to near infrared measurements of solid methane optical constants are conspicuously absent from the literature. Preliminary results are presented on the optical constants of solid methane for the 0.4 to 2.6 micrometer region. Deposition onto a substrate at 10 K produces glassy (semi-amorphous) material. Annealing this material at approximately 33 K for approximately 1 hour results in a crystalline material as seen by sharper, more structured bands and negligible background extinction due to scattering. The constant k is reported for both the amorphous and the crystalline (annealed) states. Typical values (at absorption maxima) are in the .001 to .0001 range. Below lambda = 1.1 micrometers the bands are too weak to be detected by transmission through the films less than or equal to 215 micrometers in thickness, employed in the studies to date. Using previously measured values of the real part of the refractive index, n, of liquid methane at 110 K, n is computed for solid methane using the Lorentz-Lorenz relationship. Work is in progress to extend the measurements of optical constants n and k for liquid and solid to both shorter and longer wavelengths, eventually providing a complete optical constants database for condensed CH4

Suppression of quantum tunneling for all spins for easy-axis systems

The semi-classical limit of quantum spin systems corresponds to a dynamical Lagrangian which contains the usual kinetic energy, the couplings and interactions of the spins and an additional, first order kinematical term which corresponds to the Wess-Zumino-Novikov-Witten (WZNW) term for the spin degree of freedom \cite{og}. It was shown that in the case of the kinetic dynamics determined only by the WZNW term, half odd integer spin systems show a lack of tunneling phenomena whereas integer spin systems are subject to it \cite{l} in the case of potentials with easy-plane easy-axis symmetry. Here we prove, for the theory with a normal quadratic kinetic term of arbitrary strength or the first order theory with azimuthal symmetry (which is equivalently the so-called easy-axis situation), that the tunneling is in fact suppressed for all non-zero values of spin. This model exemplifies the concept that in the presence of complex Euclidean action, it is necessary to use the ensuing complex critical points in order to define the quantum (perturbation) theory \cite{ampr}. In the present example, if we do not do so, exactly the opposite, erroneous conclusion, that the tunneling is unsuppressed for all spins, is reached.Comment: 4 pages, no figures