High resolution lifetime measurements of isolated vibronic levels in naphthalene C10H8

A frequency-doubled, continuous tunable dye laser has been employed with a bandwidth of 0.5 cm^?1 in the UV to yield high resolution dynamic information about vibronic excited states of naphthalene in the collisionless region. The results show strong variations of lifetimes in the various sequence modes identified in high resolution absorption spectra. The evidence points to a strong contribution from both Franck—Condon factors as well as symmetry considerations.     

Spectroscopy of molecular ions: Laser induced predissociation of O 2 +

The technique of laser induced predissociation and laser induced fluorescence is applied to study spectra of gas-phase molecular ions. The main feature of the experiment is a beam of mass selected molecular ions illuminated by a pulsed dye laser. Over an extended range of excitation energies spectroscopic information can be obtained about positive and negative ions including transient species. As a first result we present predissociation spectra of O ₂ ⁺ ,b ⁴ bE _g ^? ?a ⁴ π _u Δv=3 andgDv=2 which can well be simulated by calculated spectra assuming a rotational ion temperature of 300δK.     

Lower bounds for the absolute value of random polynomials on a neighborhood of the unit circle

Let where stands for a random choice of sign with equal probability. The first author recently showed that for any and most choices of sign, , provided is large. In this paper we show that the power is optimal. More precisely, for sufficiently small and large most choices of sign satisfy . Furthermore, we study the case of more general random coefficients and applications of our methods to complex zeros of random polynomials.

     

Distal charge transport in peptides

Biological systems often transport charges and reactive processes over substantial distances. Traditional models of chemical kinetics generally do not describe such extreme distal processes. In this Review, an atomistic model for a distal transport of information, which was specifically developed for peptides, is considered. Chemical reactivity is taken as the result of distal effects based on two-step bifunctional kinetics involving unique, very rapid motional properties of peptides in the subpicosecond regime. The bifunctional model suggests highly efficient transport of charge and reactivity in an isolated peptide over a substantial distance; conversely, a very low efficiency in a water environment was found. The model suggests ultrafast transport of charge and reactivity over substantial molecular distances in a peptide environment. Many such domains can be active in a protein.     

A master equation approach to the dynamics of zero electron kinetic energy (ZEKE) states and ZEKE spectroscopy

We have theoretically studied important dynamic processes involved in zero electron kinetic energy (ZEKE) spectroscopy using the density matrix method with the inverse Born-Oppenheimer approximation basis sets. In ZEKE spectroscopy, the ZEKE Rydberg states are populated by laser excitation (either a one- or two-photon process), which is followed by autoionizations and l-mixing due to a stray field. The discrimination field is then applied to ionize loosely bound electrons in the ZEKE states. This is followed by using the extraction field to extract electrons from the ZEKE levels which have a strength comparable to that of the extraction field. These extracted electrons are measured for the relative intensities of the ion states under investigation. The spectral positions are determined by the applied laser wavelength and modified by the extraction electric field. In this paper, all of these processes are conducted within the context of the density matrix method. The density matrix method can provide not only the dynamics of system's population and coherence (or phase) but also the rate constants of the processes involved in the ZEKE spectroscopy. Numerical examples are given to demonstrate the theoretical treatments.     

Global dynamics above the ground state energy for the cubic NLS equation in 3D

We extend the result in Nakanishi and Schlag (J Differ Equ 250:2299–2333, 2011) on the nonlinear Klein–Gordon equation to the nonlinear Schr?dinger equation with the focusing cubic nonlinearity in three dimensions, for radial data of energy at most slightly above that of the ground state. We prove that the initial data set splits into nine nonempty, pairwise disjoint regions which are characterized by the distinct behaviors of the solution for large time: blow-up, scattering to 0, or scattering to the family of ground states generated by the phase and scaling freedom. Solutions of this latter type form a smooth center-stable manifold, which contains the ground states and separates the phase space locally into two connected regions exhibiting blow-up and scattering to 0, respectively. The special solutions found by Duyckaerts and Roudenko (Rev Mater Iberoam 26(1):1–56, 2010), following the seminal work on threshold solutions by Duyckaerts and Merle (Funct Anal 18(6):1787–1840, 2009), appear here as the unique one-dimensional unstable/stable manifolds emanating from the ground states. In analogy with Nakanishi and Schlag (J Differ Equ 250:2299–2333, 2011), the proof combines the hyperbolic dynamics near the ground states with the variational structure away from them. The main technical ingredient in the proof is a “one-pass” theorem which precludes “almost homoclinic orbits”, i.e., those solutions starting in, then moving away from, and finally returning to, a small neighborhood of the ground states. The main new difficulty compared with the Klein–Gordon case is the lack of finite propagation speed. We need the radial Sobolev inequality for the error estimate in the virial argument. Another major difference between Nakanishi and Schlag (J Differ Equ 250:2299–2333, 2011) and this paper is the need to control two modulation parameters.     

On the Electric Field Effect on the Dynamics of High Rydberg States of Hydrogen Atom and the Model of ZEKE Spectroscopy

In this paper, the studies of the dynamics of the high Rydberg states for n = 10 and n = 100 of hydrogen atom under the influence of an electric field will be reported. It will be shown from our calculated results that the two time constants of τ_slow ≈? 1 – 10 μs and τ_fast ≈? 1 – 10 ns obseved in ZEKE experiments are obtained in the stray field condition, i.e., F = 10 – 100 mV/cm. To treat the ZEKE states of complex systems like many-electron atoms, molecules, clusters etc., the inverse Born-Oppenheimer approximation can be used and it will be discussed.