6,413 research outputs found
Spectral gaps for periodic Schr\"odinger operators with strong magnetic fields
We consider Schr\"odinger operators
with the periodic magnetic field on covering spaces of
compact manifolds. Under some assumptions on , we prove that there are
arbitrarily large number of gaps in the spectrum of these operators in the
semiclassical limit of strong magnetic field .Comment: 14 pages, LaTeX2e, xypic, no figure
Downward Collapse from a Weaker Hypothesis
Hemaspaandra et al. proved that, for and : if
\Sigma_i^p \BoldfaceDelta DIFF_m(\Sigma_k^p) is closed under complementation,
then . This sharply asymmetric
result fails to apply to the case in which the hypothesis is weakened by
allowing the to be replaced by any class in its difference
hierarchy. We so extend the result by proving that, for and : if DIFF_s(\Sigma_i^p) \BoldfaceDelta DIFF_m(\Sigma_k^p) is closed
under complementation, then
What's Up with Downward Collapse: Using the Easy-Hard Technique to Link Boolean and Polynomial Hierarchy Collapses
During the past decade, nine papers have obtained increasingly strong
consequences from the assumption that boolean or bounded-query hierarchies
collapse. The final four papers of this nine-paper progression actually achieve
downward collapse---that is, they show that high-level collapses induce
collapses at (what beforehand were thought to be) lower complexity levels. For
example, for each it is now known that if \psigkone=\psigktwo then
\ph=\sigmak. This article surveys the history, the results, and the
technique---the so-called easy-hard method---of these nine papers.Comment: 37 pages. an extended abstract appeared in SIGACT News, 29, 10-22,
199
Query Order and the Polynomial Hierarchy
Hemaspaandra, Hempel, and Wechsung [cs.CC/9909020] initiated the field of
query order, which studies the ways in which computational power is affected by
the order in which information sources are accessed. The present paper studies,
for the first time, query order as it applies to the levels of the polynomial
hierarchy. We prove that the levels of the polynomial hierarchy are
order-oblivious. Yet, we also show that these ordered query classes form new
levels in the polynomial hierarchy unless the polynomial hierarchy collapses.
We prove that all leaf language classes - and thus essentially all standard
complexity classes - inherit all order-obliviousness results that hold for P.Comment: 14 page
Self-Specifying Machines
We study the computational power of machines that specify their own
acceptance types, and show that they accept exactly the languages that
\manyonesharp-reduce to NP sets. A natural variant accepts exactly the
languages that \manyonesharp-reduce to P sets. We show that these two classes
coincide if and only if \psone = \psnnoplusbigohone, where the latter class
denotes the sets acceptable via at most one question to \sharpp followed by
at most a constant number of questions to \np.Comment: 15 pages, to appear in IJFC
Mass, radius, and composition of the outer crust of nonaccreting cold neutron stars
The properties and composition of the outer crust of nonaccreting cold
neutron stars are studied by applying the model of Baym, Pethick, and
Sutherland, which was extended by including higher order corrections of the
atomic binding, screening, exchange and zero-point energy. The most recent
experimental nuclear data from the atomic mass table of Audi, Wapstra, and
Thibault from 2003 is used. Extrapolation to the drip line is utilized by
various state-of-the-art theoretical nuclear models (finite range droplet,
relativistic nuclear field and non-relativistic Skyrme Hartree-Fock
parameterizations). The different nuclear models are compared with respect to
the mass and radius of the outer crust for different neutron star
configurations and the nuclear compositions of the outer crust.Comment: 5 pages, 2 figures, submitted to J. Phys. G, part of the proceedings
of the Nuclear Physics in Astrophysics III conference in Dresde
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