Universal Prolongation of Linear Partial Differential Equations on Filtered Manifolds

The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately to obstructions to the existence of solutions. Moreover, we will deduce that the solution space of such equations is always finite dimensional.Comment: 14 pages; v3: minor changes in section 3, typos corrected; final version to appear in Arch. math (Brno) 5, 200

Strongly essential flows on irreducible parabolic geometries

We study the local geometry of irreducible parabolic geometries admitting strongly essential flows; these are flows by local automorphisms with higher-order fixed points. We prove several new rigidity results, and recover some old ones for projective and conformal structures, which show that in many cases the existence of a strongly essential flow implies local flatness of the geometry on an open set having the fixed point in its closure. For almost c-projective and almost quaternionic structures we can moreover show flatness of the geometry on a neighborhood of the fixed point.Comment: 34 pages. Proof of Proposition 3.1 significantly shortened, under slightly less general hypotheses (see Remark 3.1). Typos corrected and references updated. To appear in Transactions of the AM

Intensity distribution in rotational line spectra

Completely resolved Doppler-free rotational line spectra of six vibronic two-photon bands in benzene C6 H6 and C6 D6 are presented. The excited final states possess different excess energies in S1 (1567 to 2727 cm−1 ) and are embedded in dense manifolds of background states with differing densities of states (1<rho<60 1/cm−1 ). The bands are analyzed by a statistical procedure. The intensity distribution of several hundreds of lines of each band is investigated. It is found that all weakly perturbed bands display a similar, peaked intensity distribution while in strongly perturbed bands the number of lines decreases monotonically with increasing intensity. The origin of this difference is discussed in terms of coupling to the many background states. The Journal of Chemical Physics is copyrighted by The American Institute of Physics

Emission spectra from single rovibronic quantum states in S1 benzene after Doppler-free two-photon excitation

Dispersed emission from single rovibronic quantum states in S1 benzene is measured after Doppler-free two-photon excitation under low pressure conditions (0.3 Torr). This was made possible by a long-term stabilization of the single-mode dye laser yielding a stability of better than 1 MHz/h. The emission spectra of unperturbed rotational levels in the 141 and the 14111 vibronic states reveal a great number of detailed results on Duschinsky rotation and long-range Fermi resonances in the electronic ground state. By contrast, it is seen that the emission spectra from perturbed rovibronic states are contaminated by additional bands. The analysis of these bands leads in most cases to an identification of the coupled dark background state and the responsible rotation–vibration coupling process (H42 resonances). The emission spectra clearly demonstrate that even for a density of states of 60 1/cm−1, coupling in S1 benzene is still selective and far from the statistical limit. It is further demonstrated that the dark and the light states are more efficiently mixed by short-range couplings with coupling matrix elements of some GHz than by long-range Fermi resonances. The Journal of Chemical Physics is copyrighted by The American Institute of Physics

High Resolution Sub-Doppler Experiments on Benzene

It is shown that sub-Doppler spectroscopy enables one to resolve individual rotational states in the S^ manifold of polyatomic molecules. This i s an essential to the understanding of the primary photophysics within the molecule. Spectra of benzene are found to undergo substantial changes as the vibrational energy i s raised within S^. Due to the increased density of vibrational states, Coriolis coupling, which is already seen at low energies, can lead to effective IVR above 3000 cm""1 excess energy. This onset of IVR may be responsible for the onset of "Channel Three" in benzene and probably produces gross changes in the photophysical behavior of any polyatomic molecule