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While several measures exist for entanglement of multipartite pure states, a true entanglement measure for mixed states still eludes us. A deeper study of the geometry of quantum states may be the way to address this issue, on which context we come up with a measure for pure states based on a geodesic distance on the space of quantum states. Our measure satisfies all the desirable properties of a ``Genuine Measure of Entanglement" (GME), and in comparison with some of the other existing measures, shows better smoothness and discriminance., Revised version, submitted to PRA

The study conducted was to characterize the acoustic features and spectrum of the Ghumot, a membranophone type musical instrument indigenous to Western India. This instrument is part of the dying culture of Goan traditional music; hence it has been studied to give it a scientific understanding. The instrument was played with both conditions of the resonance cavity taken into account (open and closed), and the frequency domain spectra were determined for each. The variation in the acoustics characteristics of the instrument was plotted according to position of impact and position of measurement. The Ghumot membrane displayed non-linear characteristics as compared to a uniform, isotropic circular membrane. A comparative study was also made for the Ghumot and the Tabla to determine the number of unique tones or ‘bols’ that the instrument can produce.

We review aspects of classical and quantum mechanics of many anyons confined in an oscillator potential. The quantum mechanics of many anyons is complicated due to the occurrence of multivalued wavefunctions. Nevertheless there exists, for arbitrary number of anyons, a subset of exact solutions which may be interpreted as the breathing modes or equivalently collective modes of the full system. Choosing the three-anyon system as an example, we also discuss the anatomy of the so called ``missing'' states which are in fact known numerically and are set apart from the known exact states by their nonlinear dependence on the statistical parameter in the spectrum. Though classically the equations of motion remains unchanged in the presence of the statistical interaction, the system is non-integrable because the configuration space is now multiply connected. In fact we show that even though the number of constants of motion is the same as the number of degrees of freedom the system is in general not integrable via action-angle variables. This is probably the first known example of a many body pseudo-integrable system. We discuss the classification of the orbits and the symmetry reduction due to the interaction. We also sketch the application of periodic orbit theory (POT) to many anyon systems and show the presence of eigenvalues that are potentially non-linear as a function of the statistical parameter. Finally we perform the semiclassical analysis of the ground state by minimizing the Hamiltonian with fixed angular momentum and further minimization over the quantized values of the angular momentum., 44 pages, one figure, eps file. References updated

The methods of reduced phase space quantization and Dirac quantization are examined in a simple gauge theory. A condition for the possible equivalence of the two methods is discussed., 8 pages. RevTex (two-column), no figures. The dvi version can be downloaded from: http://www.imsc.ernet.in/physweb/papers/radhika/pa2.dvi