319 research outputs found
Chaotic itinerancy and power-law residence time distribution in stochastic dynamical system
To study a chaotic itinerant motion among varieties of ordered states, we
propose a stochastic model based on the mechanism of chaotic itinerancy. The
model consists of a random walk on a half-line, and a Markov chain with a
transition probability matrix. To investigate the stability of attractor ruins
in the model, we analyze the residence time distribution of orbits at attractor
ruins. We show that the residence time distribution averaged by all attractor
ruins is given by the superposition of (truncated) power-law distributions, if
a basin of attraction for each attractor ruin has zero measure. To make sure of
this result, we carry out a computer simulation for models showing chaotic
itinerancy. We also discuss the fact that chaotic itinerancy does not occur in
coupled Milnor attractor systems if the transition probability among attractor
ruins can be represented as a Markov chain.Comment: 6 pages, 10 figure
Quartic double solids with ordinary singularities
We study the mixed Hodge structure on the third homology group of a threefold
which is the double cover of projective three-space ramified over a quartic
surface with a double conic. We deal with the Torelli problem for such
threefolds.Comment: 14 pages, presented at the Conference Arnol'd 7
Extending Torelli map to toroidal compactifications of Siegel space
It has been known since the 1970s that the Torelli map ,
associating to a smooth curve its jacobian, extends to a regular map from the
Deligne-Mumford compactification to the 2nd Voronoi
compactification .
We prove that the extended Torelli map to the perfect cone (1st Voronoi)
compactification is also regular, and moreover
and share a common Zariski open
neighborhood of the image of . We also show that the map to the
Igusa monoidal transform (central cone compactification) is NOT regular for
; this disproves a 1973 conjecture of Namikawa.Comment: To appear in Inventiones Mathematica
Knot homology via derived categories of coherent sheaves II, sl(m) case
Using derived categories of equivariant coherent sheaves we construct a knot
homology theory which categorifies the quantum sl(m) knot polynomial. Our knot
homology naturally satisfies the categorified MOY relations and is
conjecturally isomorphic to Khovanov-Rozansky homology. Our construction is
motivated by the geometric Satake correspondence and is related to Manolescu's
by homological mirror symmetry.Comment: 51 pages, 9 figure
Constraints on the Neutrino Mass from SZ Surveys
Statistical measures of galaxy clusters are sensitive to neutrino masses in
the sub-eV range. We explore the possibility of using cluster number counts
from the ongoing PLANCK/SZ and future cosmic-variance-limited surveys to
constrain neutrino masses from CMB data alone. The precision with which the
total neutrino mass can be determined from SZ number counts is limited mostly
by uncertainties in the cluster mass function and intracluster gas evolution;
these are explicitly accounted for in our analysis. We find that projected
results from the PLANCK/SZ survey can be used to determine the total neutrino
mass with a (1\sigma) uncertainty of 0.06 eV, assuming it is in the range
0.1-0.3 eV, and the survey detection limit is set at the 5\sigma significance
level. Our results constitute a significant improvement on the limits expected
from PLANCK/CMB lensing measurements, 0.15 eV. Based on expected results from
future cosmic-variance-limited (CVL) SZ survey we predict a 1\sigma uncertainty
of 0.04 eV, a level comparable to that expected when CMB lensing extraction is
carried out with the same experiment. A few percent uncertainty in the mass
function parameters could result in up to a factor \sim 2-3 degradation of our
PLANCK and CVL forecasts. Our analysis shows that cluster number counts provide
a viable complementary cosmological probe to CMB lensing constraints on the
total neutrino mass.Comment: Replaced with a revised version to match the MNRAS accepted version.
arXiv admin note: text overlap with arXiv:1009.411
Categorical geometric skew Howe duality
We categorify the R-matrix isomorphism between tensor products of minuscule
representations of U_q(sl(n)) by constructing an equivalence between the
derived categories of coherent sheaves on the corresponding convolution
products in the affine Grassmannian. The main step in the construction is a
categorification of representations of U_q(sl(2)) which are related to
representations of U_q(sl(n)) by quantum skew Howe duality. The resulting
equivalence is part of the program of algebro-geometric categorification of
Reshitikhin-Turaev tangle invariants developed by the first two authors.Comment: 31 page
Resonant X-Ray Magnetic Scattering from CoO
We analyze the recent experiment [W. Neubeck {\em et al.}, Phys. Rev. B
\vol(60,1999,R9912)] for the resonant x-ray magnetic scattering (RXMS) around
the K edge of Co in the antiferromagnet CoO. We propose a mechanism of the RXMS
to make the states couple to the magnetic order: the intraatomic exchange
interaction between the and the states and the - mixing to the
states of neighboring Co atoms. These couplings induce the orbital moment
in the states and make the scattering tensor antisymmetric. Using a
cluster model, we demonstrate that this modification gives rise to a large RXMS
intensity in the dipole process, in good agreement with the experiment. We also
find that the pre-edge peak is generated by the transition to the states
in the quadrupole process, with negligible contribution of the dipole process.
We also discuss the azimuthal angle dependence of the intensity.Comment: 15 pages, 8 figure
The class of the locus of intermediate Jacobians of cubic threefolds
We study the locus of intermediate Jacobians of cubic threefolds within the
moduli space of complex principally polarized abelian fivefolds, and its
generalization to arbitrary genus - the locus of abelian varieties with a
singular odd two-torsion point on the theta divisor. Assuming that this locus
has expected codimension (which we show to be true for genus up to 5), we
compute the class of this locus, and of is closure in the perfect cone toroidal
compactification, in the Chow, homology, and the tautological ring.
We work out the cases of genus up to 5 in detail, obtaining explicit
expressions for the classes of the closures of the locus of products of an
elliptic curve and a hyperelliptic genus 3 curve, in moduli of principally
polarized abelian fourfolds, and of the locus of intermediate Jacobians in
genus 5. In the course of our computation we also deal with various
intersections of boundary divisors of a level toroidal compactification, which
is of independent interest in understanding the cohomology and Chow rings of
the moduli spaces.Comment: v2: new section 9 on the geometry of the boundary of the locus of
intermediate Jacobians of cubic threefolds. Final version to appear in
Invent. Mat
- …