3,209 research outputs found

### Asymptotic analysis and spectrum of three anyons

The spectrum of anyons confined in harmonic oscillator potential shows both
linear and nonlinear dependence on the statistical parameter. While the
existence of exact linear solutions have been shown analytically, the nonlinear
dependence has been arrived at by numerical and/or perturbative methods. We
develop a method which shows the possibility of nonlinearly interpolating
spectrum. To be specific we analyse the eigenvalue equation in various
asymptotic regions for the three anyon problem.Comment: 28 pages, LaTeX, 2 Figure

### A Fermion-like description of condensed Bosons in a trap

A Bose-Einstein condensate of atoms, trapped in an axially symmetric harmonic
potential, is considered. By averaging the spatial density along the symmetry
direction over a length that preserves the aspect ratio, the system may be
mapped on to a zero temperature noninteracting Fermi-like gas. The ``mock
fermions'' have a state occupancy factor $(>>1)$ proportional to the ratio of
the coherance length to the ``hard-core'' radius of the atom. The mapping
reproduces the ground state properties of the condensate, and is used to
estimate the vortex excitation energy analytically. The ``mock-fermion''
description predicts some novel collective excitation in the condensed phase.Comment: 11 pages, REVTE

### 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

### Ground state fluctuations in finite Fermi and Bose systems

We consider a small and fixed number of fermions (bosons) in a trap. The
ground state of the system is defined at T=0. For a given excitation energy,
there are several ways of exciting the particles from this ground state. We
formulate a method for calculating the number fluctuation in the ground state
using microcanonical counting, and implement it for small systems of
noninteracting fermions as well as bosons in harmonic confinement. This exact
calculation for fluctuation, when compared with canonical ensemble averaging,
gives considerably different results, specially for fermions. This difference
is expected to persist at low excitation even when the fermion number in the
trap is large.Comment: 20 pages (including 1 appendix), 3 postscript figures. An error was
found in one section of the paper. The corrected version is updated on
Sep/05/200

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