2,200 research outputs found
Universal behaviour of ideal and interacting quantum gases in two dimensions
I discuss ideal and interacting quantum gases obeying general fractional
exclusion statistics. For systems with constant density of single-particle
states, described in the mean field approximation, the entropy depends neither
on the microscopic exclusion statistics, nor on the interaction. Such systems
are called {\em thermodynamically equivalent} and I show that the microscopic
reason for this equivalence is a one-to-one correspondence between the excited
states of these systems. This provides a method, different from the
bosonisation technique, to transform between systems of different exclusion
statistics. In the last section the macroscopic aspects of this method are
discussed.
In Appendix A I calculate the fluctuation of the ground state population of a
condensed Bose gas in grandcanonical ensemble and mean field approximation,
while in Appendix B I show a situation where although the system exhibits
fractional exclusion properties on microscopic energy intervals, a rigorous
calculation of the population of single particle states reveals a condensation
phenomenon. This also implies a malfunction of the usual and simplified
calculation technique of the most probable statistical distributions.Comment: About 14 journal pages, with 1 figure. Changes: Body of paper: same
content, with slight rephrasing. Apendices are new. In the original
submission I just mentioned the condensation, which is now detailed in
Appendix B. They were intended for a separate paper. Reason for changes:
rejection from Phys. Rev. Lett., resubmission to J. Phys. A: Math. Ge
Equation of State for Exclusion Statistics in a Harmonic Well
We consider the equations of state for systems of particles with exclusion
statistics in a harmonic well. Paradygmatic examples are noninteracting
particles obeying ideal fractional exclusion statistics placed in (i) a
harmonic well on a line, and (ii) a harmonic well in the Lowest Landau Level
(LLL) of an exterior magnetic field. We show their identity with (i) the
Calogero model and (ii) anyons in the LLL of an exterior magnetic field and in
a harmonic well.Comment: latex file, 11 page
Superfluid-Insulator transitions of bosons on Kagome lattice at non-integer fillings
We study the superfluid-insulator transitions of bosons on the Kagome lattice
at incommensurate filling factors f=1/2 and 2/3 using a duality analysis. We
find that at f=1/2 the bosons will always be in a superfluid phase and
demonstrate that the T_3 symmetry of the dual (dice) lattice, which results in
dynamic localization of vortices due to the Aharanov-Bohm caging effect, is at
the heart of this phenomenon. In contrast, for f=2/3, we find that the bosons
exhibit a quantum phase transition between superfluid and translational
symmetry broken Mott insulating phases. We discuss the possible broken
symmetries of the Mott phase and elaborate the theory of such a transition.
Finally we map the boson system to a XXZ spin model in a magnetic field and
discuss the properties of this spin model using the obtained results.Comment: 10 pages, 8 figures, a few typos correcte
Analytical theory for proton correlations in common water ice
We provide a fully analytical microscopic theory for the proton correlations
in water ice . We compute the full diffuse elastic neutron scattering
structure factor, which we find to be in excellent quantitative agreement with
Monte Carlo simulations. It is also in remarkable qualitative agreement with
experiment, in the absence of any fitting parameters. Our theory thus provides
a tractable analytical starting point to account for more delicate features of
the proton correlations in water ice. In addition, it directly determines an
effective field theory of water ice as a topological phase.Comment: 5 pages, 3 figure
Dipolar spin correlations in classical pyrochlore magnets
We study spin correlations for the highly frustrated classical pyrochlore
lattice antiferromagnets with O(N) symmetry in the limit T->0. We conjecture
that a local constraint obeyed by the extensively degenerate ground states
dictates a dipolar form for the asymptotic spin correlations, at all N 2
for which the system is paramagnetic down to T=0. We verify this conjecture in
the cases N=1 and N=3 by simulations and to all orders in the 1/N expansion
about the solvable N=infinity limit. Remarkably, the N=infinity formulae are an
excellent fit, at all distances, to the correlators at N=3 and even at N=1.
Thus we obtain a simple analytical expression also for the correlations of the
equivalent models of spin ice and cubic water ice, I_h.Comment: 4 pages revtex
Valence Bond Solids and Their Quantum Melting in Hard-Core Bosons on the Kagome Lattice
Using large scale quantum Monte Carlo simulations and dual vortex theory we
analyze the ground state phase diagram of hard-core bosons on the kagome
lattice with nearest neighbor repulsion. In contrast to the case of a
triangular lattice, no supersolid emerges for strong interactions. While a
uniform superfluid prevails at half-filling, two novel solid phases emerge at
densities and . These solids exhibit an only partial
ordering of the bosonic density, allowing for local resonances on a subset of
hexagons of the kagome lattice. We provide evidence for a weakly first-order
phase transition at the quantum melting point between these solid phases and
the superfluid.Comment: 4 pages, 7 figure
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