Quantum chaos and fractals with atoms in cavities

We study the coupled translational, electronic, and field dynamics of the combined system “a two-level atom + a single-mode quantized field + a standing-wave ideal cavity”. In the semiclassical approximation with a point-like atom, interacting with the classical field, the dynamics is described by the Heisenberg equations for the atomic and field expectation values which are known to produce semiclassical chaos under appropriate conditions. We derive Hamilton–Schrödinger equations for probability amplitudes and averaged position and momentum of a point-like atom interacting with the quantized field in a standing-wave cavity. They constitute, in general, an infinite-dimensional set of equations with an infinite number of integrals of motion which may be reduced to a dynamical system with four degrees of freedom if the quantized field is supposed to be initially prepared in a Fock state. This system is found to produce semiquantum chaos with positive values of the maximal Lyapunov exponent. At exact resonance, the semiquantum dynamics is regular. At large values of detuning |δ|1, the Rabi atomic oscillations are usually shallow, and the dynamics is found to be almost regular. The Doppler–Rabi resonance, deep Rabi oscillations that may occur at any large value of |δ| to be equal to |αp₀|, is found numerically and described analytically (with α to be the normalized recoil frequency and p₀ the initial atomic momentum). Two gedanken experiments are proposed to detect manifestations of semiquantum chaos in real experiments. It is shown that in the chaotic regime values of the population inversion z_out, measured with atoms after transversing a cavity, are so sensitive to small changes in the initial inversion z_in that the probability of detecting any value of z_out in the admissible interval [−1,1] becomes almost unity in a short time. Chaotic wandering of a two-level atom in a quantized Fock field is shown to be fractal. Fractal-like structures, typical with chaotic scattering, are numerically found in the dependence of the time of exit of atoms from the cavity on their initial momenta.     

Thee + e −→¯nn cross section predicted remarkably larger than thee + e −→¯pp one

It is shown that all global analyses of nucleon electromagnetic form factor data predict the electron-positron annihilation into neutron-antineutron cross section (for which there are no data till now) to be in a finite energy region substantially larger than the electron-positron annihilation into the proton-antiproton one.Dedicated to the memory of M. Gmitro.     

Birefringence in YAlO3∶Ce between 2–5 eV

This contribution presents birefringence spectra for orthorhombic YAlO₃Ce single crystal in the region 2–5 eV. The spectra were measured by means of a reflection method of null ellipsometry and were compared with spectra of YAlO₃:Nd determined from values measured in the region of lower energies (1·1–2·2 eV). We have found that there are differences between the spectra of YAlO₃Nd and YAlO₃:Ce which are most pronounced in thea-axis direction.The author is most grateful to Ing. . Viovský CSc. for helpful discussions during the course of this work and to Monokrystaly Turnov for preparation of the samples.     

Rapid determination of ethylene glycol at toxic levels in serum and urine

The rapid gas chromatographic detection and determination of ethylene glycol in biological fluids is described. Phenylboronic acid in acetone was used for the esterification of glycol. The phenylboronates of ethylene glycol and 1,2-propylene glycol are not separated on a packed column of medium polarity (OV-17), but they can be separated on a non-polar column (OV-101). In both instances, 1,3-propylene glycol can be used as an internal standard. The method requires only 100 microliters of serum or urine and is suitable for trace analysis in an emergency toxicological laboratory. The utility of the method is demonstrated on two cases of human intoxication with ethylene glycol.     

A viscometric study of poly(methyl methacrylate) in 2-alkoxyethanols

θ-Conditions, the temperature coefficient of unperturbed dimensions of the macromolecules and the thermodynamic interaction parameters ψ and κ were determined for solutions of poly(methyl methacrylate) in 2-alkoxyethanols (methoxy, ethoxy and butoxy). The results for this series of solvents fit the data reported for other solvents and dln $\text{r}{}_0{}^2\text{/}\text{d}\text{T = 2.6 × 10}{}^{\mathrm{?3}}\text{K}{}^{\mathrm{?1}}$. The dependence of parameters ψ and κ exhibited deviations from the theoretical dependence, mainly near the limiting value ψ = 0.5.     

The extraction of HCl by TDPO in benzene

The results of the extraction of HCl by TDPO in benzene and the co-extraction of water are discussed. From the infrared spectra of normal (HCl-H₂O) and deuterated (DCl-D₂O) systems it may be concluded that TDPO·HCl·H₂O is formed in the organic phase on extraction from aqueous solutions with c_HCl≤5M, and TDPO·HCl with c_HCl>5M. Compounds such as TDPO·2HCl are found in the organic phase if there is an excess of HCl in the organic phase. From cryoscopic and viscosity measurements of the organic phase, conclusions can be made about the presence of polymeric compounds in this phase.     

Strukturanalyse organischer Sulfide mit Hilfe der Gras-Chromatographie

Zusammenfassung Eine Methode der Identifizierung von Alkyl- und Arylgruppen organischer Sulfide wurde ausgearbeitet, die die Spaltung dieser Stoffe mit Raney-Nickel zur gaschromatographischen Bestimmung der dabei entstandenen Kohlenwasserstoffe ausnützt.

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Summary A method was developed for identifying alkyl- and aryl groups of organic sulfides. The method employs the cleavage of these materials with Raney nickel for the gas chromatographic determination of the resulting hydrocarbons.

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Résumé On a mis au point une méthode d'identification des groupes alkylés et arylés des sulfures organiques exploitant la dissociation de ceux-ci par le nickel Raney pour le dosage par chromatographic en phase gazeuse des carbures d'hydrogène qui se forment.

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Die Autoren danken den Kollegen Dr.M. Veea, Ing.J. Petránek und Ing.J. Gaspari für die Überlassung von Proben organischer Sulfide.     

Iron sites in greigite from the “Cypris series”

Results of the⁵⁷Fe Mössbauer spectroscopy of greigite from the greigite-rich horizon of the middle part of the miocene series (Sokolov Basin, North Bohemia) are reported. From the room-temperature transmission spectra of the powdered samples magnetically separated from claystones, the Mössbauer analyses were performed. Relative abundances of various magnetic and non-magnetic Fe²⁺ and Fe³⁺ species led to the identification of the two magnetic iron sites in greigite in accordance with its spinel structure having mutually near effective magnetic inductions of 32.1 and 31.3 T, respectively. In addition, three pyrrhotite and two magnetite magnetic sites plus probably two pyrite and/or arsenopyrite iron positions were identified, of which some have been reported in the literature as the greigite iron contributions.     

A model of solidification under microgravity conditions

The influence of the microgravity environment on solidification processes is discussed. A simple model of the solidification of a binary-alloy is presented with the chemical diffusion influenced by the gravitational field. Using the results of Mullins and Sekerka, we employ the linear theory of hydrodynamic stability to investigate the interfacial instability driving the pattern-forming processes in solidification. As a result, we estimate the characteristic size of the elements of the emerging pattern. We show that, in spite of good agreement of our result with the size of cellulae observed in experiments, the model cannot explain the changes in the patterns occurring in space environment. In conclusion we shortly discuss the possibility of adding realism to our simple model by including the effect of convection.