Wigner Measure Propagation and Conical Singularity for General Initial Data

We study the evolution of Wigner measures of a family of solutions of a Schrödinger equation with a scalar potential displaying a conical singularity. Under a genericity assumption, classical trajectories exist and are unique, thus the question of the propagation of Wigner measures along these trajectories becomes relevant. We prove the propagation for general initial data.     

Reiter’s Condition <Emphasis Type="Italic">P</Emphasis><Subscript>1</Subscript> and Approximate Identities for Polynomial Hypergroups

Let K be a commutative hypergroup with the Haar measure . In the present paper we investigate whether the maximal ideals in L¹(K,) have bounded approximate identities. We will show that the existence of a bounded approximate identity is equivalent to the existence of certain functionals on the space L(K,). Finally we apply the results to polynomial hypergroups and obtain a rather complete solution for this class.The third author was partially supported by KBN (Poland) under grant 5 P03A 034 20 and by Research Training Network Harmonic Analysis and Related Problems Contract HPRN-CT-2001-00273.     

Spatially incoherent illumination as a mechanism for cross-talk suppression in wide-field optical coherence tomography

Comparison of two illumination modes for wide-field optical coherence tomography has revealed that spatially coherent illumination generates coherent cross talk, causing significant image degradation, and that spatially incoherent illumination, with an adequate interferometer design, provides an efficient mechanism for suppression of coherent cross talk. This is shown by comparison of a pulsed laser with a thermal light source for a U.S. Air Force resolution target covered with a scattering solution made from microbeads as well as for an ex vivo tooth.     

Complex ambiguity-free Fourier domain optical coherence tomography through transverse scanning

We introduce a simple and cheap method for phase-shifting Fourier domain optical coherence tomography (FDOCT) that does not need additional devices and can easily be implemented. A small beam offset at the fast beam-scanning mirror introduces a causal phase shift, which can be used for B-scan-based complex image reconstruction. We derive the conditions for optimal conjugate suppression and demonstrate the method on human skin in vivo for spectrometer-based FDOCT operating at 1300 nm employing a handheld scanner.     

Single switch surface hopping for molecular quantum dynamics

The aim of this text is to present a surface hopping approximation for molecular quantum dynamics obeying a Schr?dinger equation with crossing eigenvalue surfaces. After motivating Schr?dinger equations with matrix valued potentials, we describe the single switch algorithm and present some numerical results. Then we discuss the algorithm’s mathematical justification and describe extensions to more general situations, where three eigenvalue surfaces intersect or the eigenvalues are of multiplicity two. We emphasize the generality of this surface hopping approximation for non-adiabatic transitions.     

High-speed femtosecond pump-probe spectroscopy with a smart pixel detector array

A new femtosecond pump-probe spectroscopy technique is demonstrated that permits the high-speed, parallel acquisition of pump-probe measurements at multiple wavelengths. This is made possible by use of a novel, two-dimensional smart pixel detector array that performs amplitude demodulation in real time on each pixel. This detector array can not only achieve sensitivities comparable with lock-in amplification but also simultaneously performs demodulation of probe transmission signals at multiple wavelengths, thus permitting rapid time- and wavelength-resolved femtosecond pump-probe spectroscopy. Measurements on a thin sample of bulk GaAs are performed across 58 simultaneous wavelengths. Differential probe transmission changes as small as approximately 2 x 10(-4) can be measured over a 5-ps delay scan in only approximately 3 min. This technology can be applied to a wide range of pump-probe measurements in condensed matter, chemistry, and biology.     

An alternative method for CARS-spectra calculation

We propose an alternative method for CARS-spectra calculation. This kind of spectrum-calculation allows the decomposition of the CARS-intensity into physically interpretable components. The method is based on Yuratich's analysis of effects of laser linewidth on CARS-spectroscopy. With the help of an equivalent representation of the plasma-dispersion function the CARS-intensity can be expressed via a Fourier-transform in a very easy manageable form for numerical investigations. As an example we applied our method to the Q-branch-spectrum of N₂.     

Field confinement with aberration correction for solid immersion lens based fluorescence correlation spectroscopy

The solid immersion lens (SIL) as a tool for increasing the field confinement as well as providing optimal performance by aberration compensation in a confocal fluorescence correlation spectroscopy (FCS) system is illustrated here. Using Zernike polynomials we show that aberration compensation and the resultant pre-shaping of the incident wavefront enables near diffraction-limited performance. This is explained based on vectorial computations for high apertures in the Debye approximation. The obtained axial resolution parameters are compared with the obtained diffusion times in a SIL-FCS experiment for measurements in solutions done at the single molecule level.     

EXCITED-STATE REACTIONS OF OXIDIZED FLAVIN DERIVATIVES

Abstract— The reactivity of flavin mononucleotide and of lumiflavin triplets was studied by flash and laser photolysis. The rate constants of the triplets with oxygen, with flavin ground-state molecules, and with Br^- ions were determined. Although in solution at room temperature, the protonated flavin triplet, ³F1H⁺, is not formed directly from its very short lived singlet state, a transient, which we think is this triplet, results from protonation of the neutral triplet. This conclusion is based on a comparison between the neutral and the protonated triplet spectra in a low-temperature glass. It is proposed that the protonated triplet can also be formed by sensitization via the phenanthrene triplet.