Spectral statistics of chaotic systems with a pointlike scatterer

The statistical properties of a Hamiltonian H0 perturbed by a localized scatterer are considered. We prove that if H0 describes a bounded chaotic motion, the universal part of the spectral statistics is not changed by the perturbation. This is done first within the random matrix model. Then it is shown by semiclassical techniques that the result is due to a cancellation between diagonal diffractive and off-diagonal periodic-diffractive contributions. The compensation is a very general phenomenon encoding the semiclassical content of the optical theorem.     

First experimental observation of superscars in a pseudointegrable barrier billiard

With a perturbation body technique intensity distributions of the electric field strength in a flat microwave billiard with a barrier inside up to mode numbers as large as about 700 were measured. A method for the reconstruction of the amplitudes and phases of the electric field strength from those intensity distributions has been developed. Recently predicted superscars have been identified experimentally and--using the well-known analogy between the electric field strength and the quantum mechanical wave function in a two-dimensional microwave billiard--their properties determined.     

Spectral statistics of a quantum interval-exchange map

Curious spectral properties of an ensemble of random unitary matrices appearing naturally in the quantization of a simple interval-exchange map are investigated. It is demonstrated that, under certain conditions on map parameters, local spectral statistics of this ensemble tends to the semi-Poisson distribution with arbitrary integer or half-integer level repulsion at small distances depending on time-reversal symmetry of the map.     

Spectral fluctuations and zeta functions

We study theoretically and numerically the role of the fluctuations of eigenvalue spectra {it_n in a particular analytical continuation process applied to the (generalized) zeta functionZ(s)= _{n n} ^–s fors large and positive. A particularly interesting example is the spectrum of the Laplacian on a triangular domain which tessellates a compact surface of constant negative curvature (of genus two). We indeed find that the fluctuations restrict the abscissa of convergence, and also affect the rate of convergence. This then initiates a new approach to the exploration of spectral fluctuations through the convergence of analytical continuation processes.work done while at the Service de Physique Théorique, Saclay, and Institut de Physique Nucléaire, Orsay.     

Ion/molecule reaction inside the collision cell of a tandem quadrupole mass spectrometric system. 2. Energy dependence of ammonium ion formation

The dependence of the protonation of neutral ammonia on the axial kinetic energy of protonated reactant ions has been studied in the gas phase, using various protonated carbonyl compounds, inside the collision cell of a tandem quadrupole mass spectrometric system. The hypothesis of two different and non-competitive reaction channels has been proposed. The first is characterized by a very low (peaked at ±0.05 eV_cm) and well-defined axial kinetic energy of the reactant ion, while the second is more energy demanding (estimated threshold at ±0.2 eV_cm) and expressed by a collisionally induced dissociation-like energy curve. Fourier transform mass spectrometric experiments have shown that ammonium ion can be generated by direct proton exchange and fragmentation of the adduct ion obtained.