44 research outputs found
Dynamical role of anyonic excitation statistics in rapidly rotating Bose gases
We show that for rotating harmonically trapped Bose gases in a fractional
quantum Hall state, the anyonic excitation statistics in the rotating gas can
effectively play a {\em dynamical} role. For particular values of the
two-dimensional coupling constant , where is a
positive integer, the system becomes a noninteracting gas of anyons, with
exactly obtainable solutions satisfying Bogomol'nyi self-dual order parameter
equations. Attractive Bose gases under rapid rotation thus can be stabilized in
the thermodynamic limit due to the anyonic statistics of their quasiparticle
excitations.Comment: 4 pages of RevTex4; as published in Physical Review Letter
The Universal Kummer Threefold
The universal Kummer threefold is a 9-dimensional variety that represents the
total space of the 6-dimensional family of Kummer threefolds in 7-dimensional
projective space. We compute defining polynomials for three versions of this
family, over the Satake hypersurface, over the G\"opel variety, and over the
reflection representation of type E7. We develop classical themes such as theta
functions and Coble's quartic hypersurface using current tools from
combinatorics, geometry, and commutative algebra. Symbolic and numerical
computations for genus 3 moduli spaces appear alongside toric and tropical
methods.Comment: 50 pages; v2: added Remark 4.3, strengthened Lemma 8.3; v3: added
references and added supplementary files to sourc