Three Dimensional Gauge Theory with Topological and Non-topological Mass: Hamiltonian and Lagrangian Analysis

Three dimensional (abelian) gauged massive Thirring model is bosonized in the large fermion mass limit. A further integration of the gauge field results in a non-local theory. A truncated version of that is the Maxwell Chern Simons (MCS) theory with a conventional mass term or MCS Proca theory. This gauge invariant theory is completely solved in the Hamiltonian and Lagrangian formalism, with the spectra of the modes determined. Since the vector field constituting the model is identified (via bosonization) to the fermion current, the charge current algebra, including the Schwinger term is also computed in the MCS Proca model.Comment: Eight pages, Latex, No figures

Magnetized Accretion Inside the Marginally Stable Orbit around a Black Hole

Qualitative arguments are presented to demonstrate that the energy density of magnetic fields in matter accreting onto a black hole inside the marginally stable orbit is automatically comparable to the rest-mass energy density of the accretion flow. Several consequences follow: magnetic effects must be dynamically significant, but cannot be so strong as to dominate; outward energy transport in Alfven waves may alter the effective efficiency of energy liberation; and vertical magnetic stresses in this region may contribute to "coronal" activity.Comment: to appear in Ap. J. Letter

Coherent States for the Non-Linear Harmonic Oscillator

Wave packets for the Quantum Non-Linear Oscillator are considered in the Generalized Coherent State framerwork. To first order in the non-linearity parameter the Coherent State behaves very similarly to its classical counterpart. The position expectation value oscillates in a simple harmonic manner. The energy-momentum uncertainty relation is time independent as in a harmonic oscillator. Various features, (such as the Squeezed State nature), of the Coherent State have been discussed

Planar Two-particle Coulomb Interaction: Classical and Quantum Aspects

The classical and quantum aspects of planar Coulomb interactions have been studied in detail. In the classical scenario, Action Angle Variables are introduced to handle relativistic corrections, in the scheme of time-independent perturbation theory. Complications arising due to the logarithmic nature of the potential are pointed out. In the quantum case, harmonic oscillator approximations are considered and effects of the perturbations on the excited (oscillator) states have been analysed. In both the above cases, the known 3+1-dimensional analysis is carried through side by side, for a comparison with the 2+1-dimensional (planar) results.Comment: LaTex, Figures on request, e-mail:<[email protected]

Three flavour Quark matter in chiral colour dielectric model

We investigate the properties of quark matter at finite density and temperature using the nonlinear chiral extension of Colour Dielectric Model (CCM). Assuming that the square of the meson fields devlop non- zero vacuum expectation value, the thermodynamic potential for interacting three flavour matter has been calculated. It is found that $$and$$ remain zero in the medium whereas $$ changes in the medium. As a result, $u$ and $d$ quark masses decrease monotonically as the temperature and density of the quark matter is increased.In the present model, the deconfinement density and temperature is found to be lower compared to lattice results. We also study the behaviour of pressure and energy density above critical temperature.Comment: Latex file. 5 figures available on request. To appear in Phys. Rev.

Algebraic geometric methods for the stabilizability and reliability of multivariable and of multimode systems

The extent to which feedback can alter the dynamic characteristics (e.g., instability, oscillations) of a control system, possibly operating in one or more modes (e.g., failure versus nonfailure of one or more components) is examined

Local transport in a disorder-stabilized correlated insulating phase

We report the experimental realization of a correlated insulating phase in 2D GaAs/AlGaAs heterostructures at low electron densities in a limited window of background disorder. This has been achieved at mesoscopic length scales, where the insulating phase is characterized by a universal hopping transport mechanism. Transport in this regime is determined only by the average electron separation, independent of the topology of background disorder. We have discussed this observation in terms of a pinned electron solid ground state, stabilized by mutual interplay of disorder and Coulomb interaction.Comment: 4+delta pages, 4 figures, To appear in the Physical Review B (Rapid Comm

Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions

The development in the study of supersymmetric many-particle quantum systems with inverse-square interactions is reviewed. The main emphasis is on quantum systems with dynamical OSp(2|2) supersymmetry. Several results related to exactly solved supersymmetric rational Calogero model, including shape invariance, equivalence to a system of free superoscillators and non-uniqueness in the construction of the Hamiltonian, are presented in some detail. This review also includes a formulation of pseudo-hermitian supersymmetric quantum systems with a special emphasis on rational Calogero model. There are quite a few number of many-particle quantum systems with inverse-square interactions which are not exactly solved for a complete set of states in spite of the construction of infinitely many exact eigen functions and eigenvalues. The Calogero-Marchioro model with dynamical SU(1,1|2) supersymmetry and a quantum system related to short-range Dyson model belong to this class and certain aspects of these models are reviewed. Several other related and important developments are briefly summarized.Comment: LateX, 65 pages, Added Acknowledgment, Discussions and References, Version to appear in Jouranl of Physics A: Mathematical and Theoretical (Commissioned Topical Review Article

Structural studies on encapsulation of tetrahedral and octahedral anions by a protonated octaaminocryptand cage

Structural aspects of the binding of inorganic anions such as perchlorate, hydrogen sulfate, and hexafluorosilicate with the proton cage of octaaminocryptand L1, N(CH2CH2NHCH2-p-xylyl-CH2NHCH2CH2)3N), are examined thoroughly. Crystallographic results for a hexaprotonated perchlorate complex of L1, [(H6L1)6+(ClO4-)]5(ClO4-)·11H2O·CH3CN (1), an octaprotonated hydrogen sulfate complex of L1, [(H8L1)8+(HSO4-)]7(HSO4-)·3H2O·CH3OH (2) and an octaprotonated fluorosilicate complex of L1,[(H8L1)8+(HSiF6-)]3(SiF62-)·(HSiF6-)·15H2O (3), show encapsulation of one perchlorate, hydrogen sulfate and hexafluorosilicate, respectively inside the cage of L1 in their protonated states. Further, detailed structural analysis on complex 1 reveals that the hexaprotonated L1 encapsulates a perchlorate via two N–H···O and five O–H···O hydrogen bonds from protonated secondary nitrogen atoms of L1 and lattice water molecules, respectively. Encapsulated hydrogen sulfate in complex 2 is “glued” inside the octaprotonated cage of L1 via four N–H···O and six C–H···O hydrogen bonds whereas encapsulated HSiF6− in complex 3 has short contacts via six N–H···F and three C–H···F hydrogen bonds with [H8L1]8+. In the cases of complexes 2 and 3, the cryptand L1 in octaprotonated state shows monotopic encapsulation of the guest and the final conformation of these receptors is spherical in nature compared to the elongated shape of hexaprotonated state of L1 in complex 1