Complete solutions of a family of quartic Thue and index form equations

Continuing the recent work of the second author, we prove that the diophantine equation

for has exactly 12 solutions except when , when it has 16 solutions. If denotes one of the zeros of , then for we also find all with .

     

Influence of higher harmonics of the undulator in X‐ray polarimetry and crystal monochromator design

The spectrum of the undulator radiation of beamline P01 at Petra III has been measured after passing a multiple reflection channel‐cut polarimeter. Odd and even harmonics up to the 15th order, as well as Compton peaks which were produced by the high harmonics in the spectrum, could been measured. These additional contributions can have a tremendous influence on the performance of the polarimeter and have to be taken into account for further polarimeter designs.     

Dissociative and molecular oxygen chemisorption channels on reduced rutile TiO2(110): An STM and TPD study

High-resolution scanning tunneling microscopy (STM) and temperature-programmed desorption (TPD) were used to study the interaction of O₂ with reduced TiO₂(110)–(1 × 1) crystals. STM is the technique of choice to unravel the relation between vacancy and non-vacancy assisted O₂ dissociation channels as a function of temperature. It is revealed that the vacancy-assisted, first O₂ dissociation channel is preferred at low temperature (~ 120 K), whereas the non-vacancy assisted, second O₂ dissociation channel operates at temperatures higher than 150 K–180 K. Based on the STM results on the two dissociative O₂ interaction channels and the TPD data, a new comprehensive model of the O₂ chemisorption on reduced TiO₂(110) is proposed. The model explains the relations between the two dissociative and the molecular O₂ interaction channels. The experimental data are interpreted by considering the available charge in the near-surface region of reduced TiO₂(110) crystals, the kinetics of the two O₂ dissociation channels as well as the kinetics of the diffusion and reaction of Ti interstitials.     

Forward and midrapidity charmonium production at RHIC

J/ψ production at forward and midrapidity at the Relativistic Heavy-Ion Collider (RHIC) is calculated within a previously constructed rate-equation approach accounting for both direct production and regeneration from c and . The results are compared to the experimental data. The observed stronger suppression at forward rapidity can be qualitatively explained by a smaller statistical regeneration component together with stronger cold nuclear matter induced suppression compared to midrapidity. The χ _c over J/ψ ratio and ψ′ over J/ψ ratio are also calculated.     

The nonobjectivity of past events in quantum mechanics

It is shown in this paper that a classical way of speaking about the past can be rejected when quantum systems without superselection rules are considered. To show this, use is made of a formal quantum language. The noncontextuality of quantum measurements is a presupposition of the quantum language. In addition, it is shown that introspective measurements, in contrast to the claims of Albert et al., do not violate the noncontextuality, and hence the result of rejecting the classical way of speaking remains still applicable to introspective measurements.     

Lévy Flights in a Steep Potential Well

Lévy flights in steeper than harmonic potentials have been shown to exhibit finite variance and a critical time at which a bifurcation from an initial monomodal to a terminal bimodal distribution occurs (Chechkin et al., Phys. Rev. E 67:010102(R) (2003)). In this paper, we present a detailed study of Lévy flights in potentials of the type U(x)∝|x| ^c with c>2. Apart from the bifurcation into bimodality, we find the interesting result that for c>4 a trimodal transient exists due to the temporal overlap between the decay of the central peak around the initial δ-condition and the building up of the two emerging side-peaks, which are characteristic for the stationary state. Thus, for certain system parameters there exists a transient trimodal distribution of the Lévy flight. These properties of Lévy flights in external potentials of the power-law type can be represented by certain phase diagrams. We also present details about the proof of multimodality and the numerical procedures to establish the probability distribution of the process.     

Resonant cavity photon creation via the dynamical Casimir effect

Motivated by a recent proposal for an experimental verification of the dynamical Casimir effect, the macroscopic electromagnetic field within a perfect cavity containing a thin slab with a time-dependent dielectric permittivity is quantized in terms of the dual potentials. For the resonance case, the number of photons created out of the vacuum due to the dynamical Casimir effect is calculated for both polarizations. It turns out that only TM modes can be excited efficiently.