152,746 research outputs found
Ricci flow on K\"ahler-Einstein manifolds
In our previous paper math.DG/0010008, we develop some new techniques in
attacking the convergence problems for the K\"ahler Ricci flow. The one of main
ideas is to find a set of new functionals on curvature tensors such that the
Ricci flow is the gradient like flow of these functionals. We successfully find
such functionals in case of Kaehler manifolds. On K\"ahler-Einstein manifold
with positive scalar curvature, if the initial metric has positive bisectional
curvature, we prove that these functionals have a uniform lower bound, via the
effective use of Tian's inequality. Consequently, we prove the following
theorem: Let be a K\"ahler-Einstein manifold with positive scalar
curvature. If the initial metric has nonnegative bisectional curvature and
positive at least at one point, then the K\"ahler Ricci flow will converge
exponentially fast to a K\"ahler-Einstein metric with constant bisectional
curvature. Such a result holds for K\"ahler-Einstein orbifolds.Comment: 49 pages. This is a revised version. Sections 4 and 5 are simplified
and streamline
Oxygen Isotope Effect on the Spin State Transition in (PrSm)CaCoO
Oxygen isotope substitution is performed in the perovskite cobalt oxide
(PrSm)CaCoO which shows a sharp spin
state transition from the intermediate spin (IS) state to the low spin (LS)
state at a certain temperature. The transition temperature of the spin state
up-shifts with the substitution of by O from the resistivity
and magnetic susceptibility measurements. The up-shift value is 6.8 K and an
oxygen isotope exponent () is about -0.8. The large oxygen isotope
effect indicates strong electron-phonon coupling in this material. The
substitution of O by O leads to a decrease in the frequency of
phonon and an increase in the effective mass of electron (), so that
the bandwidth W is decreased and the energy difference between the different
spin states is increased. This is the reason why the is shifted to high
temperature with oxygen isotopic exchange.Comment: 4 pages, 3 figure
Superconductivity and Phase Diagram in (LiFe)OHFeSeS
A series of (LiFe)OHFeSeS (0 x 1)
samples were successfully synthesized via hydrothermal reaction method and the
phase diagram is established. Magnetic susceptibility suggests that an
antiferromagnetism arising from (LiFe)OH layers coexists with
superconductivity, and the antiferromagnetic transition temperature nearly
remains constant for various S doping levels. In addition, the lattice
parameters of the both a and c axes decrease and the superconducting transition
temperature T is gradually suppressed with the substitution of S for Se,
and eventually superconductivity vanishes at = 0.90. The decrease of T
could be attributed to the effect of chemical pressure induced by the smaller
ionic size of S relative to that of Se, being consistent with the effect of
hydrostatic pressure on (LiFe)OHFeSe. But the detailed
investigation on the relationships between and the crystallographic
facts suggests a very different dependence of on anion height from
the Fe2 layer or -Fe2- angle from those in FeAs-based superconductors.Comment: 6 pages, 6 figure
Lattice theory of finite-size effects above the upper critical dimension
We present a perturbative calculation of finite-size effects near of
the lattice model in a -dimensional cubic geometry of size with
periodic boundary conditions for . The structural differences between
the lattice theory and the field theory found previously in
the spherical limit are shown to exist also for a finite number of components
of the order parameter. The two-variable finite-size scaling functions of the
field theory are nonuniversal whereas those of the lattice theory are
independent of the nonuniversal model parameters.One-loop results for
finite-size scaling functions are derived. Their structure disagrees with the
single-variable scaling form of the lowest-mode approximation for any finite
where is the bulk correlation length. At , the large-
behavior becomes lowest-mode like for the lattice model but not for the
field-theoretic model. Characteristic temperatures close to of the
lattice model, such as of the maximum of the susceptibility
, are found to scale asymptotically as ,
in agreement with previous Monte Carlo (MC) data for the five-dimensional Ising
model. We also predict asymptotically. On a
quantitative level, the asymptotic amplitudes of this large - behavior close
to have not been observed in previous MC simulations at because
of nonnegligible finite-size terms caused by the
inhomogeneous modes. These terms identify the possible origin of a significant
discrepancy between the lowest-mode approximation and previous MC data. MC data
of larger systems would be desirable for testing the magnitude of the
and terms predicted by our theory.Comment: Accepted in Int. J. Mod. Phys.
Maximal Acceleration Corrections to the Lamb Shift of Muonic Hydrogen
The maximal acceleration corrections to the Lamb shift of muonic hydrogen are
calculated by using the relativistic Dirac wave functions. The correction for
the transition is meV and is higher than the accuracy of
present QED calculations and of the expected accuracy of experiments in
preparation.Comment: LaTex file, 9 pages, to be published in Il Nuovo Cimento
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