Features of the quasienergy spectrum of the hydrogen atom in a microwave field

The nearest neighbour level spacing of the quasienergies of a hydrogen atom in a micro-wave field is studied. There is evidence of level repulsion among states corresponding to classically chaotic regions. In the regions of classical phase space where the motion is approximately regular, the corresponding quasienergy spectrum can be understood in terms of approximate dynamical constants. In particular, grouping the high lying quasienergy states into photons yields level spacing plots that are close to δ functions; there is little fluctuation about the average value predicted by the approximate constant. The grouping suggests a simple explanation of the “photon localization” recently observed by Casati et al. [1].     

Microwave ionization of highly excited hydrogen atoms

Within a 1-dimensional model we calculate quantum mechanically the probability to ionize a highly excited hydrogen atom by a monochromatic microwave field. Based on a detailed analysis of the ionization process we developed a computational scheme as well as a simple physical framework which are presented and discussed. Our calculations are in good agreement with the experimental results. We show that the experimentally measured ionization thresholds are due to a sharp transition between two localization regimes and that recently measured structures below the classical chaos border are due to unresolved clusters of Floquet pseudo crossings. We propose an experimental method by which one could measure the distance and distribution of crossing Floquet eigenvalues.     

Decomposability of polytopes and polyhedra

In this paper decomposability of polytopes (and polyhedral sets) is studied by investigating the space of affine dependences of the vertices of the dual polytope. This turns out to be a fruitful approach and leads to several new results, as well as to simpler proofs and generalizations of known results. One of the new results is that a 3-polytope with more vertices than facets is decomposable; this leads to a characterization of the decomposability of 3-polytopes.     

Nuclear deformations from inelastic α-scattering on rare earth nuclei at energies near the Coulomb barrier

Alpha particles in the energy range of 10–20 MeV and scattered at various angles were used to excite the 0⁺, 2⁺, 4⁺ members in the ground state bands of ¹⁵²Sm, ¹⁵⁴Sm and ¹⁸⁶W. The measured excitation probabilities for bombarding energies below the Coulomb barrier were analyzed in the framework of Coulomb excitation theory. The resulting matrix elements of the E2 and E4 multipole operators were interpreted in terms of charge deformation parameters β^cλ = 2, 4. The cross sections for higher energies were analyzed in terms of the deformed optical potential and resulted in potential deformation parameters β^pλ = 2, 4. The two sets of deformation parameters show the same general trend of variation with target mass number. Still, significant differences are observed in some particular cases.     

Resolving the isospectrality of the dihedral graphs by counting nodal domains

We discuss isospectral quantum graphs which are not isometric. These graphs are the analogues of the isospectral domains in R² which were introduced recently in [1–5] all based on Sunada's construction of isospectral domains [6]. After discussing some of the properties of these graphs, we present an example which support the conjecture that by counting the nodal domains of the corresponding eigenfunctions one can resolve the isospectral ambiguity.     

Dynamics of Nodal Points and the Nodal Count on a Family of Quantum Graphs

We investigate the properties of the zeros of the eigenfunctions on quantum graphs (metric graphs with a Schr?dinger-type differential operator). Using tools such as scattering approach and eigenvalue interlacing inequalities we derive several formulas relating the number of the zeros of the n-th eigenfunction to the spectrum of the graph and of some of its subgraphs. In a special case of the so-called dihedral graph we prove an explicit formula that only uses the lengths of the edges, entirely bypassing the information about the graph??s eigenvalues. The results are explained from the point of view of the dynamics of zeros of the solutions to the scattering problem.