Spin-orbit interaction in molecular photoelectron spectra An intermediate coupling approach

A new and general semiempirical method for calculating ionization energies of molecules containing heavy atoms is presented. The extended Hückel hamiltonian is amended with a phenomenological one-electron spin-orbit interaction operator, and ionization energies are equated to orbital energies according to Koopmans' theorem. Calculations are presented for molecules with Br and I as heavy atoms. The systems considered are the hydrogen halides, diatomic halogens and interhalogens, haloacetylenes, halomethanes, and boron trihalides. Good agreement with the observed spin-orbit splitting is obtained. New assignments are proposed for the trihalides considered.     

Divergencies in a vector model with hyperbolic symmetry on a chain

A chain of interacting vectors (, ) withn components subject to the hyperbolic conditions ²–²=1 is considered. The interaction possesses a global non-compactO(1, n–1)/O(1)×O(n–1) symmetry. Symmetries of this kind are known from the study of disordered electronic systems. The non-compactness of the symmetry group causes divergencies such that a symmetry breaking term is necessary. Asymptotic behaviour of the expectation values and long-ranged correlation functions are calculated for a small symmetry breaking field.Supported in part by the Deutsche Forschungsgemeinschaft through the Sonderforschungsbereich 123 at the University of Heidelberg     

Diffusive clustering in an infinite system of hierarchically interacting diffusions

Summary We study a countable system of interacting diffusions on the interval [0,1], indexed by a hierarchical group. A particular choice of the interaction guaranties, we are in the diffusive clustering regime. This means clusters of components with values either close to 0 or close to 1 grow on various different scales. However, single components oscillate infinitely often between values close to 0 and close to 1 in such a way that they spend fraction one of their time together and close to the boundary. The processes in the whole class considered and starting with a shift-ergodic initial law have the same qualitative properties (universality).     

SiO2 surface defect centers studied by AES

A theoretical model is proposed on how a Si dangling bond associated with an oxygen vacancy on a SiO₂ surface (E_s′ center) should be observed by Auger electron spectroscopy (AES). The Auger electron distribution N_A(E) for the L₂₃VV transition band is calculated for a stoichiometric SiO₂ surface, and for a SiO_x surface containing Si-(e^?O₃) coordinations. The latter is characterized by an additional L₂₃VD transition band, where D is the energy level of the unpaired electron e^?. The theoretical N_A(E) spectra are compared with experimental N(E) spectra for a pristine, and for an electron radiation damaged quartz surface. Agreement with the theoretical model is obtained if D is assumed to lie ≈2 eV below the conduction band edge. This result shows that AES is uniquely useful in revealing the absolute energy level of localized, occupied surface defect states. As the L₂₃VD transition band (main peak at 86 eV) cannot unambiguously be distinguished from a SiSi₄ coordination L₂₃VV spectrum (main peak at 88 eV), supporting evidence is presented as to why we exclude a SiSi₄ coordination for our particular experimental example. Application of the Si-(e^?O₃) model to the interpretation of SiO₂Si interface Auger spectra is also discussed.     

There are no scalar Lie fields in three or more dimensional space-time

We show that a Lie field structure is incompatible with a scalar relativistic quantum field theory if the dimension of space-time is greater than two. Our main argument is based on the Jacobi identity and the spectrum condition.     

Minimal nicht überauflösbare,endliche Gruppen

Ohne Zusammenfassung     

T-Periodic solutions of time dependent Hamiltonian systems with a potential vanishing at infinity

We are discussing existence and multiplicity of T-periodic solutions of the time dependent Hamiltonian system = U(x, t) under the assumption that U(x, t) approaches 0 for large |x| meaning that the force U is concentrated in a finite region. Our method is variational and it is shown how the difficulties with the Palais-Smale condition can be overcome in this case.     

Stochastic integrators with stationary independent increments

Summary Lipschitzian stochastic differential equations driven by a process with stationary independent increments permit a priori growth and stability estimates up to any sure time, and the solutions depend differentiably on parameters provided the Levy measure of the driving term has suitable moments.Research partially supported by NSF grant Nr. MCS 8001779     

Jaynes-Cummings dynamics with a matter wave oscillator

We propose to subject two Bose-Einstein condensates to a periodic potential, so that one condensate undergoes the Mott-insulator transition to a state with precisely one atom per lattice site. We show that photoassociation of heteronuclear molecules within each lattice site is described by the quantum optical Jaynes-Cummings Hamiltonian. In analogy with studies of this Hamiltonian with cavity fields and trapped ions, we are thus able to engineer quantum optical states of atomic matter wave fields and we are able to reconstruct these states by quantum state tomography.     

Time evolution of Wikipedia network ranking

X-ray circular magnetic dichroism, polarized neutron diffraction, ac susceptibility, and Seebeck effect have been measured for several members of the RCo₂ series (R = Ho, Tm, Er) as a function of temperature and applied magnetic field. The experimental results show robust parimagnetism (a general behaviour along the RCo₂ series with R being a heavy rare earth ion) and two reversal temperatures in some systems, which is an unexpected result. Polarised neutron diffraction show differences between results obtained on single crystals or polycrystalline ingots. We propose an interpretation of parimagnetic RCo₂ as a Griffiths phase of the high temperature, magnetically ordered, amorphous RCo₂ phase.