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     

Exponential weak Bernoulli mixing for collet-eckmann maps

We prove exponential weak Bernoulli mixing for invariant measures of certain piecewise monotone interval maps studied in [BK] and [KN]. In particular we prove this for unimodal maps with negative Schwarzian derivative satisfying lim , wherec is the unique critical point ofT.     

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).     

The α transition in Fe1−xMxS materials (M = Mn,Cr): Physical and structural aspects

For Fe_1?xM_xS, the NiAs-type solid solution is limited to x < 0.12, and the materials exhibit a low-temperature FeS-type behavior with an α transition. Fe_1?xM_xS, the low-temperature solid solution is limited to x < 0.08, and for higher Cr concentration a high-temperature FeS-type behavior is observed. Resistivities and magnetic susceptibilities reveal the progressive weakening of the α transition for increasing Mn or Cr concentration.Crystal structure determination of Fe_0.96Mn_0.04S and Fe_0.955Cr_0.045S establish that the superstructure (a√3, 2c) weakening is due to the formation of disordered domains induced by the M substitutions.Physical and structural results are discussed together and lead to an interpretation of the α transition, whether induced by temperature or impurities, as a transition between a nondegenerated polaron gas, at low temperature or for x_Cr < 0.08, and a degenerated polaron gas for T > T_α or for x_Cr > 0.08. The validity of this polaron model is discussed in the case of Fe_1?xM_xS.     

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     

The isotopes259106,260106, and261106

In irradiations of²⁰⁷Pb and²⁰⁸Pb, respectively, with⁵⁴Cr theα-decay of the isotopes²⁵⁹106,²⁶⁰106, and²⁶¹106 could be observed for the first time. For²⁶⁰106 a spontaneous fission branch of (50 _?20 ⁺³⁰ )% was observed. The isotopes were identified by genetic relationships of α-decay after separation in-flight with the velocity filter SHIP and implantation into a position-sensitive silicon surface-barrier detector. The measured partial fission halflife of the doubly even isotope²⁶⁰106 of (7.2 _?2.7 ^+4.8 )ms exceeds the predicted values by at least a factor of 40. This result could be explained by the high shell corrections of the ground state mass, derived from the measured α-decay energies. The experimental results show evidence for an island of purely shell stabilized nuclei in the region of deformed isotopes beyond the actinides.     

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.