Global Range Estimates for Maximal Oscillatory Integrals with Radial Testfunctions

We consider the maximal function of oscillatory integrals and prove a global estimate for radial test functions which is almost sharp with respect to the Sobolev regularity.Comment: Preprints in Mathematical Sciences 2011:1 ISSN 1403-9338, LUNFMA-5068-201

Intensity-intensity correlations as a probe of interferences - under conditions of none in the intensity

The different behaviour of first order interferences and second order correlations are investigated for the case of two coherently excited atoms. For intensity measurements this problem is equivalent to Young's double slit experiment and was investigated in an experiment by Eichmann et al. [Phys. Rev. Lett. 70, 2359 (1993)] and later analyzed in detail by Itano et al. [Phys. Rev. A 57, 4176 (1998)]. Our results show that in cases where the intensity interferences disappear the intensity-intensity correlations can display an interference pattern with a visibility of up to 100%. The contrast depends on the polarization selected for the detection and is independent of the strength of the driving field. The nonclassical nature of the calculated intensity-intensity correlations is also discussed.Comment: 14 pages, 2 figure

Nanosecond Dynamics of Single-Molecule Fluorescence Resonance Energy Transfer

Motivated by recent experiments on photon statistics from individual dye pairs planted on biomolecules and coupled by fluorescence resonance energy transfer (FRET), we show here that the FRET dynamics can be modelled by Gaussian random processes with colored noise. Using Monte-Carlo numerical simulations, the photon intensity correlations from the FRET pairs are calculated, and are turned out to be very close to those observed in experiment. The proposed stochastic description of FRET is consistent with existing theories for microscopic dynamics of the biomolecule that carries the FRET coupled dye pairs.Comment: 8 pages, 1 figure. accepted to J.Phys.Chem.

Regularity, Decay, and Best Constants for Dispersive Equations

AbstractWe show that the Strichartz L2w(L2)-estimates for solutions to the (pseudo-) differential equations−Δxu=i∂tuand−Δx +1u=i∂tu are equivalent. A necessary and sufficient condition for decay and regularity for solutions to the equationϕ(−Δx)u=i∂tu is given