Families of Line-Graphs and Their Quantization

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L ⁿ (G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour.     

Leçons de Mathématiques générales

Monatshefte für Mathematik -     

Two-step photoionization of Na2: dependence on alignment

Laser light is used for two-step photoionization of Na₂. the first step depends on the moleculer orientation, the second step doesnot. This yields a method for the analysis of molecular alignment.     

Operation of KrF and ArF tunable excimer lasers without Cassegrain optics

A commercial tunable excimer laser consists of an oscillator-amplifier combination. The oscillator produces high-quality light that is sent to the amplifier and is distributed throughout the amplifier cavity via Cassegrain optics. We describe here two alternative approaches, a single-pass configuration for use with KrF and a triple-pass configuration with ArF, both of which do away with the Cassegrain optics. In each approach, the beam energy is the same as with Cassegrain optics. For KrF, the changes provide better locking, a higher degree of linear polarization, and a better spatial beam homogeneity, but a poorer beam divergence. For ArF, there is also better beam homogeneity, but the locking efficiency and divergence are not as good as with Cassegrain optics.     

Charge location and fragmentation under electron impact. IV—the behaviour under electron impact of some N-methyl,N′-R-1,2,4-phosphadiazetidine-3-ones and related compounds

The ionization potentials of a series of N-methyl,N′-R-1,2,4-phosphadiazetidine-3-ones and related compounds have been determined. The nature of the highest occupied orbital of the molecules and the use of empirical rules to rationalize the variations in the ionization potentials are discussed. The changes in the fragmentation patterns are related to the different low ionization potential site(s) in each molecule. The occurrence of various rearrangement ions are discussed on a similar basis.