78,145 research outputs found
Gevrey estimates of the resolvent and sub-exponential time-decay of solutions
In this article, we study a class of non-selfadjoint Schr{\"o}dinger
operators H which are perturbation of some model operator H 0 satisfying a
weighted coercive assumption. For the model operator H 0 , we prove that the
derivatives of the resolvent satisfy some Gevrey estimates at threshold zero.
As application, we establish large time expansions of semigroups e --tH and e
--itH for t > 0 with subexponential time-decay estimates on the remainder,
including possible presence of zero eigenvalue and real resonances
Large-time asymptotics of solutions to the Kramers-Fokker-Planck equation with a short-range potential
In this work, we use scattering method to study the Kramers-Fokker-Planck
equation with a potential whose gradient tends to zero at the infinity. For
short-range potentials in dimension three, we show that complex eigenvalues do
not accumulate at low-energies and establish the low-energy resolvent
asymptotics. This combined with high energy pseudospectral estimates valid in
more general situations gives the large-time asymptotics of the solution in
weighted spaces
Inflation and Alternatives with Blue Tensor Spectra
We study the tilt of the primordial gravitational waves spectrum. A hint of
blue tilt is shown from analyzing the BICEP2 and POLARBEAR data. Motivated by
this, we explore the possibilities of blue tensor spectra from the very early
universe cosmology models, including null energy condition violating inflation,
inflation with general initial conditions, and string gas cosmology, etc. For
the simplest G-inflation, blue tensor spectrum also implies blue scalar
spectrum. In general, the inflation models with blue tensor spectra indicate
large non-Gaussianities. On the other hand, string gas cosmology predicts blue
tensor spectrum with highly Gaussian fluctuations. If further experiments do
confirm the blue tensor spectrum, non-Gaussianity becomes a distinguishing test
between inflation and alternatives.Comment: 13 pages, 10 figures. v2: references and minor improvements added.
v3: version to appear on JCA
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