6,900 research outputs found
A conjectural generating function for numbers of curves on surfaces
I give a conjectural generating function for the numbers of -nodal
curves in a linear system of dimension on an algebraic surface. It
reproduces the results of Vainsencher for the case and
Kleiman-Piene for the case . The numbers of curves are expressed
in terms of five universal power series, three of which I give explicitly as
quasimodular forms. This gives in particular the numbers of curves of arbitrary
genus on a K3 surface and an abelian surface in terms of quasimodular forms,
generalizing the formula of Yau-Zaslow for rational curves on K3 surfaces. The
coefficients of the other two power series can be determined by comparing with
the recursive formulas of Caporaso-Harris for the Severi degrees in . We
verify the conjecture for genus 2 curves on an abelian surface. We also discuss
a link of this problem with Hilbert schemes of points.Comment: amslatex 13 page
On a filtered multiplicative basis of group algebras
Let be a field of characteristic and a nonabelian metacyclic
finite -group. We give an explicit list of all metacyclic -groups ,
such that the group algebra over a field of characteristic has a
filtered multiplicative -basis. We also present an example of a
non-metacyclic 2-group , such that the group algebra over any field of
characteristic 2 has a filtered multiplicative -basis.Comment: 10 pages, AMS-Te
X-ray and optical observations of three clusters of galaxies: Abell 901, Abell 1437, and Abell 3570
We analyse three clusters of galaxies, Abell 901 (z=0.17), Abell 1437
(z=0.13) and Abell 3570 (z=0.037). They have low to intermediate X-ray fluxes
and an irregular morphology in the ROSAT All-Sky Survey (RASS). These clusters
are chosen to test the abilities and limitations of the RASS in terms of
cluster fluxes and cluster morphologies. Therefore some ``worst'' cases are
used here. X-ray observations with the ROSAT/HRI and optical spectroscopic
observations are carried out. The ROSAT/HRI observations, which have a much
better spatial resolution than the RASS, reveal in two of the three cases a
significantly different morphology than seen in the RASS. The reasons are point
sources which could not be resolved in the RASS and were therefore confused
with the cluster emission. For A3570 we could confirm the relaxed state of the
cluster by the optical determination of a small velocity dispersion. In the
cluster with the lowest flux (Abell 901) the countrate measurement is strongly
affected by point sources, in the two other cases the countrate measurements of
the RASS are reliable, i.e. they are reproduced by the ROSAT/HRI measurement.
We conclude that for clusters with a flux of a few times 10^{-12} erg/cm^2/s or
smaller, which show at the same time a non-relaxed morphology, the flux
measurement of the RASS can be seriously affected by fore- or background
sources. We point out that an all-sky survey of a second ABRIXAS mission would
provide a much clearer source distinction for low-flux clusters and thus a much
improved countrate determination.Comment: 8 pages (incl. 6 figures), accepted for publication in A&A (Suppl.
Critical exponents at the superconductor-insulator transition in dirty-boson systems
I obtain the inverse of the correlation length exponent at the
superfluid-Bose glass quantum critical point as a series in small parameter
, with d being the dimensionality of the system, and compute the
first two terms using a novel field-theoretic technique. For d=2 I find and , for short-range and Coulomb interactions between
bosons, respectively. When combined with the exact values of the dynamical
critical exponents and , these results are in quantitative
agreement with the experiments on onset of superfluidity in in porous
glasses, and on superconductor-insulator transition in homogeneous metallic
films, in support of the dirty-boson theory fot the latter. Higher-order
calculation of the exponents and of the universal conductivity is discussed.Comment: 4 pages, RevTex, eq. 10 correcte
Extension of the Brinkman-Rice picture and the Mott transition
In order to explain the metal-Mott-insulator transition, the Brinkman-Rice
(BR) picture is extended. In the case of less than one as well as one electron
per atom, the on-site Coulomb repulsion is given by U={kappa}{rho}^2U_c by
averaging the electron charge per atom over all atomic sites, where {kappa} is
the correlation strength of U, {rho} is the band filling factor, and U_c is the
critical on-site Coulomb energy. The effective mass of a quasiparticle is found
to be m*/m=1/{1-{kappa}^2{rho}^4} for 0<{kappa}{rho}^2<1 and seems to follow
the heat capacity data of Sr_{1-x}La_xTiO_3 and YBa_2Cu_3O_{7-delta} at
{kappa}=1 and 0<{kappa}{rho}^2<1. The Mott transition of the first order occurs
at {kappa}{rho}^2=1 and a band-type metal-insulator transition takes place at
{kappa}{rho}^2=0. This Mott transition is compared with that in the d=infinity
Hubbard model. The effective mass for 2D-DOS instead of the vHs can be used for
the mechanism of high T_c superconductivity.Comment: RevTex, Physica C, Vol. 341-348, 259-260 (2000
Neutrino Experiments : Highlights
This article consists of two parts. The first section presents the highlights
on the goals of neutrino physics, status of the current neutrino experiments
and future directions and program. The second section describes the theme,
program and research efforts for the TEXONO Collaboration among scientists from
Taiwan and China.Comment: 7 pages, 7 figure; Invited Contributions to the Proceedings of ``The
Fifth International Workshop on Particle Physics Phenomenology (PPP2000)'
Spin twists, domain walls, and the cluster spin-glass phase of weakly doped cuprates
We examine the role of spin twists in the formation of domain walls, often
called stripes, by focusing on the spin textures found in the cluster spin
glass phases of LaSrCuO and YCaBaCuO. To this end, we derive an analytic
expression for the spin distortions produced by a frustrating bond, both near
the core region of the bond and in the far field, and then derive an expression
for interaction energies between such bonds. We critique our analytical theory
by comparison to numerical solutions of this problem and find excellent
agreement. By looking at collections of small numbers of such bonds localized
in some region of a lattice, we demonstrate the stability of small ``clusters''
of spins, each cluster having its own orientation of its antiferromagnetic
order parameter. Then, we display a domain wall corresponding to spin twists
between clusters of locally ordered spins showing how spin twists can serve as
a mechanism for stripe formation. Since the charges are localized in this
model, we emphasize that these domain walls are produced in a situation for
which no kinetic energy is present in the problem.Comment: 19 pages, revtex, 10 eps figures (2 of which (figs. 8 and 10) are
colour
Roton Instability of the Spin Wave Excitation in the Fully Polarized Quatum Hall State and the Phase Diagram at
We consider the effect of interactions on electrons confined to two
dimensions at Landau level filling , with the specific aim to determine
the range of parameters where the fully polarized state is stable. We calculate
the charge and the spin density collective modes in random phase approximation
(RPA) including vertex corrections (also known as time dependent Hartree Fock),
and treating the Landau level mixing accurately within the subspace of a single
particle hole pair. It is found that the spin wave excitation mode of the fully
polarized state has a roton minimum which deepens as a result of the
interaction induced Landau level mixing, and the energy of the roton vanishes
at a critical Zeeman energy signaling an instability of the fully polarized
state at still lower Zeeman energies. The feasibility of the experimental
observation of the roton minimum in the spin wave mode and its softening will
be discussed. The spin and charge density collective modes of the unpolarized
state are also considered, and a phase diagram for the state as a
function of and the Zeeman energy is obtained.Comment: 47 pages, 9 figure
Doppler shift on local density of states and local impurity scattering in the vortex state
The vortex state thermal and transport properties of the high T_c copper
oxides can be understood in a d-wave gap model and are dominated by the
extended quasiparticle states that exist along the nodal directions in momentum
space. The Doppler shift on these states due to the circulating supercurrents
around the vortex core, introduces new van Hove ridges into the energy
dependent local density of states (LDOS) as a function of distance in the
region between cores. We emphasize the topology of these ridges and the effect
on them of local impurity scattering in Born and unitary limit. We treat
possible orthorhombicity. Effective local scttering rates are also obtaines.Comment: 19 pages, 7 Figure
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