Collisions for the quantum Coulomb Hamiltonian

We study the propagation of phase space singularities for the time dependent Schrödinger equation with potential having Coulomb-type singularities in space dimension equal tothree. We prove that the singularities (frequency set) of the solution are reflected by a Coulomb center exactly as in the classical problem, i.e. the frequency set follows theregularized trajectories of Classical Mechanics after a collision.     

Differential Response of Pentanal and Hexanal Exhalation to Supplemental Oxygen and Mechanical Ventilation in Rats

High inspired oxygen during mechanical ventilation may influence the exhalation of the previously proposed breath biomarkers pentanal and hexanal, and additionally induce systemic inflammation. We therefore investigated the effect of various concentrations of inspired oxygen on pentanal and hexanal exhalation and serum interleukin concentrations in 30 Sprague Dawley rats mechanically ventilated with 30, 60, or 93% inspired oxygen for 12 h. Pentanal exhalation did not differ as a function of inspired oxygen but increased by an average of 0.4 (95%CI: 0.3; 0.5) ppb per hour, with concentrations doubling from 3.8 (IQR: 2.8; 5.1) ppb at baseline to 7.3 (IQR: 5.0; 10.8) ppb after 12 h. Hexanal exhalation was slightly higher at 93% of inspired oxygen with an average difference of 0.09 (95%CI: 0.002; 0.172) ppb compared to 30%. Serum IL-6 did not differ by inspired oxygen, whereas IL-10 at 60% and 93% of inspired oxygen was greater than with 30%. Both interleukins increased over 12 h of mechanical ventilation at all oxygen concentrations. Mechanical ventilation at high inspired oxygen promotes pulmonary lipid peroxidation and systemic inflammation. However, the response of pentanal and hexanal exhalation varies, with pentanal increasing by mechanical ventilation, whereas hexanal increases by high inspired oxygen concentrations.     

Suche nach Strahlungsprozessen zweiter Ordnung beim Zerfall von Ag109m

The decay of an excited state by the emission of twoγ-quanta (γ γ-transitions) or two conversion electrons (e e-transitions) or oneγ-quantum and one conversion electron (γ e-transitions) is expected as a second order radiation process. The decay of Ag^109m was examined for such events using a special arrangement of two NaJ-scintillation counters in coincidence. The energies of coincident quanta were displayed on the two axes of an “X-Y”-Oscilloscope respectively. For the ratio ofγ γ-transitions to one-quantum transitions an upper limit of\(\frac{{W_{\gamma \gamma } }}{{W_\gamma }} \leqq 1,9 \cdot 10^{ - 5} \) was obtained. Furthermore theγ-spectrum in coincidence withK X-rays was studied. From these measurementse e- andγ e-transition rates can be calculated for the case ofK shell conversion. The results obtained are:

$$\frac{{W_{^e K^e K} }}{{W_\gamma }} = \left( {8,1_{ - 1,7}^{ + 0,6} } \right) \cdot 10^{ - 3} and\frac{{W_{\gamma ^e K} }}{{W_\gamma }}< 1,5 \cdot 10^{ - 3} .$$     

Generalized Farey Trees,Transfer Operators and Phase Transitions

We consider a family of Markov maps on the unit interval, interpolating between the tent map and the Farey map. The latter is not uniformly expanding. Each map being composed of two fractional linear transformations, the family generalizes many particular properties which for the case of the Farey map have been successfully exploited in number theory. We analyze the dynamics through the spectral properties of the generalized transfer operator. Application of the thermodynamic formalism to the family reveals first and second order phase transitions and unusual properties like positivity of the interaction function.     

The Hannay angles: Geometry,adiabaticity, and an example

The Hannay angles were introduced by Hannay as a means of measuring a holonomy effect in classical mechanics closely corresponding to the Berry phase in quantum mechanics. Using parameter-dependent momentum mappings we show that the Hannay angles are the holonomy of a natural connection. We generalize this effect to non-Abelian group actions and discuss non-integrable Hamiltonian systems. We prove an averaging theorem for phase space functions in the case of general multi-frequency dynamical systems which allows us to establish the almost adiabatic invariance of the Hannay angles. We conclude by giving an application to celestial mechanics.Supported by the Deutsche ForschungsgemeinschaftSupported by the Akademie der Wissenschaften zu Berlin