29,694 research outputs found
Quantum Phases and Collective Excitations in Bose-Hubbard Models with Staggered Magnetic Flux
We study the quantum phases of a Bose-Hubbard model with staggered magnetic
flux in two dimensions, as has been realized recently [Aidelsburger {\it et
al.}, PRL, {\bf 107}, 255301 (2011)]. Within mean field theory, we show how the
structure of the condensates evolves from weak to strong coupling limit,
exhibiting a tricritical point at the Mott-superfluid transition. Non-trivial
topological structures (Dirac points) in the quasi-particle (hole) excitations
in the Mott state are found within random phase approximation and we discuss
how interaction modifies their structures. Excitation gap in the Mott state
closes at different points when approaching the superfluid states,
which is consistent with the findings of mean field theory.Comment: 5 pages, 3 figure
A comparison of the accuracy of saddlepoint conditional cumulative distribution function approximations
Consider a model parameterized by a scalar parameter of interest and a
nuisance parameter vector. Inference about the parameter of interest may be
based on the signed root of the likelihood ratio statistic R. The standard
normal approximation to the conditional distribution of R typically has error
of order O(n^{-1/2}), where n is the sample size. There are several
modifications for R, which reduce the order of error in the approximations. In
this paper, we mainly investigate Barndorff-Nielsen's modified directed
likelihood ratio statistic, Severini's empirical adjustment, and DiCiccio and
Martin's two modifications, involving the Bayesian approach and the conditional
likelihood ratio statistic. For each modification, two formats were employed to
approximate the conditional cumulative distribution function; these are
Barndorff-Nielson formats and the Lugannani and Rice formats. All
approximations were applied to inference on the ratio of means for two
independent exponential random variables. We constructed one and two-sided
hypotheses tests and used the actual sizes of the tests as the measurements of
accuracy to compare those approximations.Comment: Published at http://dx.doi.org/10.1214/074921707000000193 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
- …