6,649 research outputs found
Torus invariant divisors
Using the language of polyhedral divisors and divisorial fans we describe
invariant divisors on normal varieties X which admit an effective codimension
one torus action. In this picture X is given by a divisorial fan on a smooth
projective curve Y. Cartier divisors on X can be described by piecewise affine
functions h on the divisorial fan S whereas Weil divisors correspond to certain
zero and one dimensional faces of it. Furthermore we provide descriptions of
the divisor class group and the canonical divisor. Global sections of line
bundles O(D_h) will be determined by a subset of a weight polytope associated
to h, and global sections of specific line bundles on the underlying curve Y.Comment: 16 pages; 5 pictures; small changes in the layout, further typos
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Structure of resonance eigenfunctions for chaotic systems with partial escape
Physical systems are often neither completely closed nor completely open, but instead are best described by dynamical systems with partial escape or absorption. In this paper we introduce classical measures that explain the main properties of resonance eigenfunctions of chaotic quantum systems with partial escape. We construct a family of conditionally invariant measures with varying decay rates by interpolating between the natural measures of the forward and backward dynamics. Numerical simulations in a representative system show that our classical measures correctly describe the main features of the quantum eigenfunctions: their multifractal phase-space distribution, their product structure along stable and unstable directions, and their dependence on the decay rate. The (Jensen-Shannon) distance between classical and quantum measures goes to zero in the semiclassical limit for long- and short-lived eigenfunctions, while it remains finite for intermediate cases
Re-Examination of Possible Bimodality of GALLEX Solar Neutrino Data
The histogram formed from published capture-rate measurements for the GALLEX
solar neutrino experiment is bimodal, showing two distinct peaks. On the other
hand, the histogram formed from published measurements derived from the similar
GNO experiment is unimodal, showing only one peak. However, the two experiments
differ in run durations: GALLEX runs are either three weeks or four weeks
(approximately) in duration, whereas GNO runs are all about four weeks in
duration. When we form 3-week and 4-week subsets of the GALLEX data, we find
that the relevant histograms are unimodal. The upper peak arises mainly from
the 3-week runs, and the lower peak from the 4-week runs. The 4-week subset of
the GALLEX dataset is found to be similar to the GNO dataset. A recent
re-analysis of GALLEX data leads to a unimodal histogram.Comment: 14 pages, 8 figure
Prevalence of marginally unstable periodic orbits in chaotic billiards
The dynamics of chaotic billiards is significantly influenced by coexisting
regions of regular motion. Here we investigate the prevalence of a different
fundamental structure, which is formed by marginally unstable periodic orbits
and stands apart from the regular regions. We show that these structures both
{\it exist} and {\it strongly influence} the dynamics of locally perturbed
billiards, which include a large class of widely studied systems. We
demonstrate the impact of these structures in the quantum regime using
microwave experiments in annular billiards.Comment: 6 pages, 5 figure
The Fallacy of Averages
This is the publisher's version, also available electronically from http://www.jstor.org/stable/2461871?seq=1#page_scan_tab_contents.No abstract is available for this item
Nonequilibrium electron spin polarization in a double quantum dot. Lande mechanism
In moderately strong magnetic fields, the difference in Lande g-factors in
each of the dots of a coupled double quantum dot device may induce oscillations
between singlet and triplet states of the entangled electron pair and lead to a
nonequilibrium electron spin polarization. We will show that this polarization
may partially survive the rapid inhomogeneous decoherence due to random nuclear
magnetic fields.Comment: New version contains figures. New title better reflects the content
of the pape
Roots of the affine Cremona group
Let k[x_1,...,x_n] be the polynomial algebra in n variables and let A^n=Spec
k[x_1,...,x_n]. In this note we show that the root vectors of the affine
Cremona group Aut(A^n) with respect to the diagonal torus are exactly the
locally nilpotent derivations x^a\times d/dx_i, where x^a is any monomial not
depending on x_i. This answers a question due to Popov.Comment: 4 page
Electroweak Supersymmetry with an Approximate U(1)_PQ
A predictive framework for supersymmetry at the TeV scale is presented, which
incorporates the Ciafaloni-Pomarol mechanism for the dynamical determination of
the \mu parameter of the MSSM. It is replaced by (\lambda S), where S is a
singlet field, and the axion becomes a heavy pseudoscalar, G, by adding a mass,
m_G, by hand. The explicit breaking of Peccei-Quinn (PQ) symmetry is assumed to
be sufficiently weak at the TeV scale that the only observable consequence is
the mass m_G. Three models for the explicit PQ breaking are given; but the
utility of this framework is that the predictions for all physics at the
electroweak scale are independent of the particular model for PQ breaking. Our
framework leads to a theory similar to the MSSM, except that \mu is predicted
by the Ciafaloni-Pomarol relation, and there are light, weakly-coupled states
in the spectrum. The production and cascade decay of superpartners at colliders
occurs as in the MSSM, except that there is one extra stage of the cascade
chain, with the next-to-LSP decaying to its "superpartner" and \tilde{s},
dramatically altering the collider signatures for supersymmetry. The framework
is compatible with terrestrial experiments and astrophysical observations for a
wide range of m_G and . If G is as light as possible, 300 keV < m_G < 3 MeV,
it can have interesting effects on the radiation energy density during the
cosmological eras of nucleosynthesis and acoustic oscillation, leading to
predictions for N_{\nu BBN} and N_{\nu CMB} different from 3.Comment: 45 pages, 2 colour figures, a reference added, minor correction
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