7,539 research outputs found
On the (non)rigidity of the Frobenius Endomorphism over Gorenstein Rings
It is well-known that for a large class of local rings of positive
characteristic, including complete intersection rings, the Frobenius
endomorphism can be used as a test for finite projective dimension. In this
paper, we exploit this property to study the structure of such rings. One of
our results states that the Picard group of the punctured spectrum of such a
ring cannot have -torsion. When is a local complete intersection,
this recovers (with a purely local algebra proof) an analogous statement for
complete intersections in projective spaces first given in SGA and also a
special case of a conjecture by Gabber. Our method also leads to many simply
constructed examples where rigidity for the Frobenius endomorphism does not
hold, even when the rings are Gorenstein with isolated singularity. This is in
stark contrast to the situation for complete intersection rings. Also, a
related length criterion for modules of finite length and finite projective
dimension is discussed towards the end.Comment: Minor changes in Example 2.2 and Theorem 2.9. Conjecture 1.2 was
added
Probing the isovector transition strength of the low-lying nuclear excitations induced by inverse kinematics proton scattering
A compact approach based on the folding model is suggested for the
determination of the isoscalar and isovector transition strengths of the
low-lying () excitations induced by inelastic proton
scattering measured with exotic beams. Our analysis of the recently measured
inelastic O+p scattering data at and 43 MeV/nucleon
has given for the first time an accurate estimate of the isoscalar
and isovector deformation parameters (which cannot be determined from
the (p,p') data alone by standard methods) for 2 and excited
states in O. Quite strong isovector mixing was found in the 2
inelastic O+p scattering channel, where the strength of the isovector
form factor (prototype of the Lane potential) corresponds to a
value almost 3 times larger than and a ratio of nuclear transition
matrix elements .Comment: 5 pages, 3 figure
Spin-chirality decoupling in the one-dimensional Heisenberg spin glass with long-range power-law interactions
We study the issue of the spin-chirality decoupling/coupling in the ordering
of the Heisenberg spin glass by performing large-scale Monte Carlo simulations
on a one-dimensional Heisenberg spin-glass model with a long-range power-law
interaction up to large system sizes. We find that the spin-chirality
decoupling occurs for an intermediate range of the power-law exponent.
Implications to the corresponding -dimensional short-range model is
discussed.Comment: 5 pages, 4 figures, to appear in Physical Review Letter
Monte Carlo studies of the chiral and spin orderings of the three-dimensional Heisenberg spin glass
The nature of the ordering of the three-dimensional isotropic Heisenberg spin
glass with nearest-neighbor random Gaussian coupling is studied by extensive
Monte Carlo simulations. Several independent physical quantities are measured
both for the spin and for the chirality, including the correlation-length
ratio, the Binder ratio, the glass order parameter, the overlap distribution
function and the non-self-averageness parameter. By controlling the effect of
the correction-to-scaling, we have obtained a numerical evidence for the
occurrence of successive chiral-glass and spin-glass transitions at nonzero
temperatures, T_{CG} > T_{SG} > 0. Hence, the spin and the chirality are
decoupled in the ordering of the model. The chiral-glass exponents are
estimated to be \nu_{CG}=1.4+-0.2 and \eta_{CG}=0.6+-0.2, indicating that the
chiral-glass transition lies in a universality class different from that of the
Ising spin glass. The possibility that the spin and chiral sectors undergo a
simultaneous Kosterlitz-Thouless-type transition is ruled out. The chiral-glass
state turns out to be non-self-averaging, possibly accompanying a one-step-like
peculiar replica-symmetry breaking. Implications to the chirality scenario of
experimental spin-glass transitions are discussed.Comment: 20 pages, 24 figures. The Chi^2-analysis of the transition point has
been added with new Fig.12. Some references also adde
Solar generation and storage of O2 (a 1 delta g)
An investigation was performed of the technical steps required to design a solar powered oxygen-iodine laser. Singlet delta oxygen is formed upon transfer of energy from selected photoexcited dye molecules to ground state molecular oxygen and then is concentrated and stored as an endoperoxide by reaction with an aromatic hydrocarbon. The endoperoxide, when heated, releases singlet oxygen in high yield thus providing a regenerable source of laser fuel. Energy transfer from dye molecules to molecular oxygen was investigated. When dye molecules were adsorbed to polymer substrates it was observed that the dye became embedded in the polymer matrix. Porphin dyes were incorporated into films of 1,4-dimethyl-2-poly(vinylnaphthalene), 2PVN. An endoperoxide was formed when porphin-doped 2PVN was exposed to visible radiation. This demonstrates the possibility of generating singlet oxygen using solar energy and concentrating and storing it in one simple step. Transport of energy by exciton migration in polycrystalline dye films was also investigated
Isospin dependence of 6He+p optical potential and the symmetry energy
A consistent folding analysis of the elastic p(6He,6He)p scattering and
charge exchange p(6He,6Li*)n reaction data measured at Elab=41.6A MeV has been
performed within the coupled channels formalism. We have used the isovector
coupling to link the isospin dependence of 6He+p optical potential to the cross
section of p(6He,6Li*)n reaction exciting the 0+ isobaric analog state (IAS) at
3.563 MeV in 6Li. Based on these results and the Hartree-Fock calculation of
asymmetric nuclear matter using the same isospin-dependent effective
nucleon-nucleon interaction, we were able to confirm that the most realistic
value of the symmetry energy Esym is around 31 MeV. Our analysis has also shown
that the measured charge exchange p(6He,6Li*)n data are quite sensitive to the
halo tail of the 6He density used in the folding calculation and the IAS of 6Li
is likely to have a halo structure similar to that established for the ground
state of 6He.Comment: Accepted for publication in Phys. Rev.
Neutron transition strengths of states in the neutron rich Oxygen isotopes determined from inelastic proton scattering
A coupled-channel analysis of the O data has been
performed to determine the neutron transition strengths of 2 states in
Oxygen targets, using the microscopic optical potential and inelastic form
factor calculated in the folding model. A complex density- and \emph{isospin}
dependent version of the CDM3Y6 interaction was constructed, based on the
Brueckner-Hatree-Fock calculation of nuclear matter, for the folding model
input. Given an accurate isovector density dependence of the CDM3Y6
interaction, the isoscalar () and isovector () deformation
lengths of 2 states in O have been extracted from the
folding model analysis of the data. A specific -dependence of
and has been established which can be linked to the
neutron shell closure occurring at approaching 16. The strongest isovector
deformation was found for 2 state in O, with about 2.5
times larger than , which indicates a strong core polarization by the
valence neutrons in O. The ratios of the neutron/proton transition
matrix elements () determined for 2 states in O have
been compared to those deduced from the mirror symmetry, using the measured
values of 2 states in the proton rich Ne and Mg
nuclei, to discuss the isospin impurity in the excitation of the
and isobars.Comment: Version accepted for publication in Physical Review
Quantum phase transitions in disordered dimerized quantum spin models and the Harris criterion
We use quantum Monte Carlo simulations to study effects of disorder on the
quantum phase transition occurring versus the ratio g=J/J' in square-lattice
dimerized S=1/2 Heisenberg antiferromagnets with intra- and inter-dimer
couplings J and J'. The dimers are either randomly distributed (as in the
classical dimer model), or come in parallel pairs with horizontal or vertical
orientation. In both cases the transition violates the Harris criterion,
according to which the correlation-length exponent should satisfy nu >= 1. We
do not detect any deviations from the three-dimensional O(3) universality class
obtaining in the absence of disorder (where nu = 0.71). We discuss special
circumstances which allow nu<1 for the type of disorder considered here.Comment: 4+ pages, 3 figure
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