17,684 research outputs found
Measurement of the neutron electric dipole moment by crystal diffraction
An experiment using a prototype setup to search for the neutron electric
dipole moment by measuring spin-rotation in a non-centrosymmetric crystal
(quartz) was carried out to investigate statistical sensitivity and systematic
effects of the method. It has been demonstrated that the concept of the method
works. The preliminary result of the experiment is ecm. The experiment showed that an accuracy of ecm can be obtained in 100 days data taking, using available
quartz crystals and neutron beams.Comment: 13 pages, 4 figure
Algebraic Closed Geodesics on a Triaxial Ellipsoid
We propose a simple method of explicit description of families of closed
geodesics on a triaxial ellipsoid that are cut out by algebraic surfaces in
. Such geodesics are either connected components of spatial
elliptic curves or rational curves.
Our approach is based on elements of the Weierstrass--Poncar\'e reduction
theory for hyperelliptic tangential covers of elliptic curves and the addition
law for elliptic functions.
For the case of 3-fold and 4-fold coverings, explicit formulas for the
cutting algebraic surfaces are provided and some properties of the
corresponding geodesics are discussed.Comment: 15 figure
Biphoton ququarts as either pure or mixed states, features and reconstruction from coincidence measurements
Features of biphoton polarization-frequency ququarts are considered. Their
wave functions are defined as functions of both polarization and frequency
variables of photons with the symmetry obligatory for two-boson states taken
into account. In experiments, biphoton ququarts can display different features
in dependence on whether experiments involve purely polarization or
(alternatively) polarization-frequency measurements. If in experiments one uses
only polarization measurements, the originally pure states of ququarts can be
seen as mixed biphoton polarization states. Features of such states are
described and discussed in details. Schemes of coincidence measurements for
reconstruction of the ququart's parameters are suggested and described
On the Grothendieck-Serre Conjecture about principal bundles and its generalizations
Let be a regular connected affine semi-local scheme over a field . Let
be a reductive group scheme over . Assuming that has an appropriate
parabolic subgroup scheme, we prove the following statement. Given an affine
-scheme , a principal -bundle over is trivial if it is
trivial over the generic fiber of the projection . We also
simplify the proof of the Grothendieck-Serre conjecture: let be a regular
connected affine semi-local scheme over a field . Let be a reductive
group scheme over . A principal -bundle over is trivial if it is
trivial over the generic point of . We generalize some other related results
from the simple simply-connected case to the case of arbitrary reductive group
schemes.Comment: Final version to be published in the Journal of Algebra and Number
Theory. We slightly change the isotropy condition as well as the terminology:
see Definition 1.1 of strongly locally isotropic reductive groups. We remove
the assumption that U is geometrically regular in Theorem 1 (regular is
enough). Other minor improvement
Resonances in three-body systems with short and long-range interactions
The complex scaling method permits calculations of few-body resonances with
the correct asymptotic behaviour using a simple box boundary condition at a
sufficiently large distance. This is also valid for systems involving more than
one charged particle. We first apply the method on two-body systems. Three-body
systems are then investigated by use of the (complex scaled) hyperspheric
adiabatic expansion method. The case of the 2 resonance in Be and
Li is considered. Radial wave functions are obtained showing the correct
asymptotic behaviour at intermediate values of the hyperradii, where wave
functions can be computed fully numerically.Comment: invited talk at the 18th International Conference on Few-Body
Problems in Physics, Santos-S.Paulo, August 21-26, 200
On the Grothendieck-Serre conjecture on principal bundles in mixed characteristic
Let R be a regular local ring. Let G be a reductive R-group scheme. A
conjecture of Grothendieck and Serre predicts that a principal G-bundle over R
is trivial if it is trivial over the quotient field of R. The conjecture is
known when R contains a field. We prove the conjecture for a large class of
regular local rings not containing fields in the case when G is split.Comment: Minor corrections and improvement
Affine Grassmannians of group schemes and exotic principal bundles over A¹
Let G be a simple simply-connected group scheme over a regular local scheme
U. Let E be a principal G-bundle over A^1_U trivial away from a subscheme
finite over U. We show that E is not necessarily trivial and give some criteria
of triviality. To this end we define affine Grassmannians for group schemes and
study their Bruhat decompositions for semi-simple group schemes. We also give
examples of principal G-bundles over A^1_U with split G such that the bundles
are not isomorphic to pull-backs from U.Comment: Introduction re-written. Other minor improvements. Final versio
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