Incipience of quantum chaos in the spin-boson model

The peculiar spectral properties of the spinboson model make it suitable for an investigation of quantum nonintegrability effects and level statistics from a new perspective. For fixed spin quantum numbers, its energy spectrum consists of 2s+1 sequences of levels with no upper bound. These sequences are identified and labelled consecutively by means of a quantum invariant calculated from the time average of a non-stationary operator. For integrable cases, level repulsion (on the energy axis) is limited to states within each sequence. From the observed spectral properties, we infer a series ofs-dependent level-spacing distributions. They converge towards a Poisson distribution fors. For nonintegrable cases, level repulsion becomes a universal phenomenon, but the amount of repulsion between two states decreases with increasing separation (in label) of the two sequences to which they belong. For smalls, the quantum nonintegrability effects are compelling but not at all chaotic. Nevertheless, they contain all the ingredients necessary to produce the symptoms commonly described as indicators of quantum chaos. In this model, we can observe quantum chaos in the making under very controllable conditions.     

Coupling of the GB set property for ergodic averages

Let (Y,,,T) be an ergodic dynamical system. LetA be an nonempty subset ofL ²() such that , whereA=sup{||sȒt||₂ ,s, tA} andN(A, u) is the smallest number ofL ²()-open balls of radiusu, centered inA, enough to coverA. Let . We prove as a consequence of a more general result, thatC(A) is aGB subset ofL ²().     

How to improve transmissive optics in the very far infrared?

Conclusion We have presented the possibility to make optical coatings on quartz in the FIR and we have got a transmission coefficient as high as 97% at room temperature. It will rise probably close to 100% at liquid helium temperature where the quartz two-phonon difference processes are frozen. The use of polyethylene or TPX is also possible to make plates and lenses. The reflectivity losses are smaller because the refractive index is much smaller, but they cannot be further reduced by any coating because there is no transparent material with n1.2 in the FIR. These lenses are very useful in the FIR (except around 60 cm^–1 if they are made of polyethylene). TPX is quite transparent over the whole FIR range, and also in the visible with nearly the same refractive index as in the FIR. Alignments can be made with visible light, and still work in the FIR.     

Modular curves and Poncelet polygons

Parts of the results and the essential techniques of this note are taken from the Erlangen thesis (1991) of the second author. They were circulated as Nr. 122 of Schriftenreihe Komplexe Mannigfaltigkeiten. Our research was supported by DFG grant Ba 423/3-3 and the European Science Project Geometry of Algebraic Varieties SCI-0398-C(A)     

Negative ion mass spectra of some unsaturated C-glycosides following keV ion bombardment

A series of anomeric unsaturated C-glycosides were studied by negative ion mass spectrometry following keV ion bombardment The compounds bearing an acidic hydrogen show a prominent [M ? H]^? peak; in the other cases, the [M ? H]^? peak is of very low intensity. A retro-Diels–Alder fragmentation and the abstraction of a hydrogen atom from the aglycon residue are observed in all cases.     

Thermodynamics of mixtures of hexane and heptane isomers with normal and branched hexadecane

Molar excess mixing enthalpies h ^E , Gibbs free energies g ^E and hence entropies s ^E have been obtained using calorimetry and the vapor sorption method at 25°C for hexane isomers+2,2,4,4,6,8,8-heptamethylnonane, a highly branched C ₁₆ . The h ^E and g ^E are negative while Ts ^E are positive, but small. The values are explained by the Prigogine-Flory theory through negative free volume contributions to h ^E and Ts ^E , counterbalanced in the case of Ts ^E by the positive combinatiorial Ts ^E for mixing molecules of different size. No contribution is seen from the interaction between methyl and methylene groups. The excess quantities are also obtained for hexane and heptane isomers mixed with n-hexadecane. Values of h ^E and Ts ^E are now strongly positive, while those of g ^E are only slightly less negative. The interpretation requires two recently advanced contributions in addition to those of the Prigogine-Flory theory: 1) a decrease of order when correlations of orientations between n-C ₁₆ molecules in the pure liquid are replaced in the solution by weaker correlations whose strengths depend on the shapes of the lower alkane isomers. For lower alkane isomers of the same shape, but highly sterically hindered, h ^E and Ts ^E are small, manifesting, 2) a negative contribution, ascribed to a rotational ordering of n-C ₁₆ segments on the sterically-hindered molecule. Enthalpy-entropy compensation is observed for these new contributions, arising from their rapid fall-off with increase of temperature.     

Mécanisme de la réaction de cyclisation en milieu aqueux de carbanilates de propargyle en méthylène-4 oxazolidinones-2

The alkaline hydrolysis of propargyl 3-chlorocarbanilates was investigated kinetically using uv spectropotometry. The cyclization to 4-methoylene-2-oxazolisinones proceeds via the numcleophilic attack of the substrate anion concomitantly with that of the hydroxide ion on the triple bond. The nucleophilic attack leads directly to the heterocycle whereas the hydroxide ion attack gives rise to a ketocarbamate which is then cyclized to the oxazolidione.