11 research outputs found

### Reduction of Anyons to One Dimension and Calogero-Sutherland-type Models

The two-dimensional anyon system, when reduced to one dimension, yields
models related to the Calogero-Sutherland model. One such reduction leads to a
new model with a class of exact solutions. This model is one of a family of
models obtained upon dimensional reduction of spherically symmetric models in
arbitrary dimensions.Comment: 12 pages, no Figures, to appear in IJMP

### Some Remarks on the Quantization of Gauge Theories

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.Comment: 8 pages. RevTex (two-column), no figures. The dvi version can be
downloaded from: http://www.imsc.ernet.in/physweb/papers/radhika/pa2.dv

### Einstein's Recoiling Slit Experiment, Complementarity and Uncertainty

We analyze Einstein's recoiling slit experiment and point out that the
inevitable entanglement between the particle and the recoiling-slit was not
part of Bohr's reply. We show that if this entanglement is taken into account,
one can provided a simpler answer to Einstein. We also derive the
Englert-Greenberger-Yasin duality relation from this entanglement. In addition,
we show that the Englert-Greenberger-Yasin duality relation can also be thought
of as a consequence of the sum uncertainty relation for certain observables of
the recoiling slit. Thus, the uncertainty relations and entanglement are both
an integral part of the which-way detection process.Comment: 7 pages, closest to the published versio

### Classical and Quantum Mechanics of Anyons

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.Comment: 44 pages, one figure, eps file. References update

### Study of Sarasvati Veena â€“ a South Indian musical instrument using its vibro-acoustic signatures

This study aims to characterize and standardize the Sarasvati Veena of South India. The instrument is very unique in the way in which it is manufactured and played. This instrument is often tuned relative to the accompanying instruments. The aim of the study was to find out the optimum tuning frequency for a particular Veena. The natural frequency of the body of the Veena was determined by conducting an impact test. The strings of the Veena were tuned to the corresponding body frequency to obtain resonance and FFT plots were generated to see the frequency variation. The optimum tuning frequency for a given Veena was obtained such that the body undergoes conductive resonance when tuned to that particular frequency. Acoustic readings were taken using a sound level meter to confirm on the results obtained by impact test

### A Note on Fermion and Gauge Couplings in Field Theory Models for Tachyon Condensation

We study soliton solutions in supersymmetric scalar field theory with a class
of potentials. We study both bosonic and fermionic zero-modes around the
soliton solution. We study two possible couplings of gauge fields to these
models. While the Born-Infeld like coupling has one normalizable mode (the zero
mode), the other kind of coupling has no normalizable modes. We show that
quantum mechanical problem which determines the spectrum of fluctuation modes
of the scalar, fermion and the gauge field is identical. We also show that only
the lowest lying mode, i.e., the zero mode, is normalizable and the rest of the
spectrum is continuous.Comment: 10 pages, 2 figures, LaTe

### Classical Many-particle Clusters in Two Dimensions

We report on a study of a classical, finite system of confined particles in
two dimensions with a two-body repulsive interaction. We first develop a simple
analytical method to obtain equilibrium configurations and energies for few
particles. When the confinement is harmonic, we prove that the first transition
from a single shell occurs when the number of particles changes from five to
six. The shell structure in the case of an arbitrary number of particles is
shown to be independent of the strength of the interaction but dependent only
on its functional form. It is also independent of the magnetic field strength
when included. We further study the effect of the functional form of the
confinement potential on the shell structure. Finally we report some
interesting results when a three-body interaction is included, albeit in a
particular model.Comment: Minor corrections, a few references added. To appear in J. Phys:
Condensed Matte