134 research outputs found
Asymptotically exact trial wave functions for yrast states of rotating Bose gases
We revisit the composite fermion (CF) construction of the lowest angular
momentum yrast states of rotating Bose gases with weak short range interaction.
For angular momenta at and below the single vortex, , the overlaps
between these trial wave functions and the corresponding exact solutions {\it
increase} with increasing system size and appear to approach unity in the
thermodynamic limit. In the special case , this remarkable behaviour was
previously observed numerically. Here we present methods to address this point
analytically, and find strongly suggestive evidence in favour of similar
behaviour for all . While not constituting a fully conclusive proof
of the converging overlaps, our results do demonstrate a striking similarity
between the analytic structure of the exact ground state wave functions at , and that of their CF counterparts. Results are given for two different
projection methods commonly used in the CF approach
Few-electron artificial molecules formed by laterally coupled quantum rings
We study the artificial molecular states formed in laterally coupled double
semiconductor nanorings by systems containing one, two and three electrons. An
interplay of the interring tunneling and the electron-electron interaction is
described and its consequences for the magnetization and charging properties of
the system are determined. It is shown that both the magnetic dipole moment
generated by the double ring structure and the chemical potential of the system
as function of the external magnetic field strongly depend on the number of
electrons and the interring barrier thickness. Both the magnetization and
chemical potentials exhibit cusps at the magnetic fields inducing ground-state
parity and / or spin transformations. The symmetry transformations are
discussed for various tunnel coupling strengths: from rings coupled only
electrostatically to the limit of coalesced rings. We find that in the
ground-states for rings of different radii the magnetic field transfers the
electron charge from one ring to the other. The calculations are performed with
the configuration interaction method based on an approach of Gaussian functions
centered on a rectangular array of points covering the studied structure.
Electron-electron correlation is also discussed
Ideal quantum gases in two dimensions
Thermodynamic properties of non-relativistic bosons and fermions in two
spatial dimensions and without interactions are derived. All the virial
coefficients are the same except for the second, for which the signs are
opposite. This results in the same specific heat for the two gases. Existing
equations of state for the free anyon gas are also discussed and shown to break
down at low temperatures or high densities.Comment: 17 page
Model of statistically coupled chiral fields on the circle
Starting from a field theoretical description of multicomponent anyons with
mutual statistical interactions in the lowest Landau level, we construct a
model of interacting chiral fields on the circle, with the energy spectrum
characterized by a symmetric matrix with nonnegative entries.
Being represented in a free form, the model provides a field theoretical
realization of (ideal) fractional exclusion statistics for particles with
linear dispersion, with as a statistics matrix. We derive the
bosonized form of the model and discuss the relation to the effective
low-energy description of the edge excitations for abelian fractional quantum
Hall states in multilayer systems.Comment: 26 pages, Latex, 1 Latex figure included. The figure has been
correcte
Few-electron eigenstates of concentric double quantum rings
Few-electron eigenstates confined in coupled concentric double quantum rings
are studied by the exact diagonalization technique. We show that the magnetic
field suppresses the tunnel coupling between the rings localizing the
single-electron states in the internal ring, and the few-electron states in the
external ring. The magnetic fields inducing the ground-state angular momentum
transitions are determined by the distribution of the electron charge between
the rings. The charge redistribution is translated into modifications of the
fractional Aharonov-Bohm period. We demonstrate that the electron distribution
can be deduced from the cusp pattern of the chemical potentials governing the
single-electron charging properties of the system. The evolution of the
electron-electron correlations to the high field limit of a classical Wigner
molecule is discussed.Comment: to appear in Physical Review
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