Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation

This paper is a direct continuation of [1] where we began the study of the integrable structures in Conformal Field Theory. We show here how to construct the operators ${\bf Q}_{\pm}(\lambda)$ which act in the highest weight Virasoro module and commute for different values of the parameter λ. These operators appear to be the CFT analogs of the Q - matrix of Baxter [2], in particular they satisfy Baxter's famous T- Q equation. We also show that under natural assumptions about analytic properties of the operators as the functions of λ the Baxter's relation allows one to derive the nonlinear integral equations of Destri-de Vega (DDV) [3] for the eigenvalues of the Q-operators. We then use the DDV equation to obtain the asymptotic expansions of the Q - operators at large λ; it is remarkable that unlike the expansions of the T operators of [1], the asymptotic series for Q(λ) contains the “dual” nonlocal Integrals of Motion along with the local ones. We also discuss an intriguing relation between the vacuum eigenvalues of the Q - operators and the stationary transport properties in the boundary sine-Gordon model. On this basis we propose a number of new exact results about finite voltage charge transport through the point contact in the quantum Hall system. Received: 2 December 1996 / Accepted: 11 March 1997     

Field evaporation and field desorption from HTSC single-crystal surfaces

The problems of field evaporation (FE) and field desorption (FD) from surface of oxide high-temperature superconductors (HTSC) of 123, 2212 and 2223 type are discussed. Wide-angle atom probe, usual time-of-flight atom probe and field ionization magnet mass-spectrometer have been used in these experiments. The main purpose of the investigation was to search for effects connected with phase transition. Therefore, the experiments were carried out over a wide range of temperatures: from T of solid nitrogen to room T.

Composition of pure, contaminated and deep corroded surface and typical species of FE and FD spectra have been studied. The bond energies between some atoms (or clusters) and the surface have been estimated on the basis of experimental results and FE theory. From these estimations, and from discovering of correlated ion pairs, it was concluded that the redistribution of local bonds should be taken into consideration in this case. The increase of FE rate was observed at cryogenic temperatures. Various versions are discussed to explain these effects. Some of them are connected with phase transition.

A detailed study of FD of water protonized clusters is performed and the catalytic activity of HTSC crystal surfaces is discussed.     

Matrix Lax Polynomials, Geometry of Prym Varieties and Systems of Hess–Appel’rot Type

We consider a four-dimensional generalization of Hess–Appel’rot system and costruct its Lax pair. Both classical and algebro-geometric integration procedure are proceeded. The algebro-geometric integration is based on deep facts from geometry of Prym varieties such as the Mumford relation and Mumford-Dalalyan theory. The integration is similar to the integration of Lagrange bitop which has recetly been performed by the authors.     

SO42-/Zr-ZSM-5 超强酸催化剂的制备和表征

以硅溶胶和氧氯化锆为硅源和锆源，采用水热合成的方法制得具有ZSM-5结构的Zr-Si分子筛；用0.5mol/L的硫酸处理该分子筛，并在550℃焙烧，制得具有ZSM-5结构的SO4^2-/ZrO2-SiO2分子筛型的固体超强酸。采用XRD、SEM、TG、IR、NH3-PHD和指示剂法对其结构和酸性进行表征。结果表明，该SO4^2-/ZrO2-SiO2具有ZSM-5结构和超强酸性，其酸强度大于-13.75，且具有良好的热稳定性。     

Stereochemie von Metallocenen, 40. Mitt.

Starting from optically active methylferrocene-- and--carboxylic acids (1 a and1 b) of known absolute configuration and enantiomeric purity about 15 chiral ferrocenes (of each isomeric series— and ) were obtained by suitable ligand transformations. Thereby (almost) all possible chiral combinations of the ligands CH₃, COOH (COO^–), COOCH₃, CN and NH₂ (NH₃ ⁺) were accessible which are necessary for a potential test of approximations of chirality functions for compounds with basic symmetry C_5v. The chiroptical properties of these disubstituted ferrocenes are recorded.Preliminary tests using a shortened Ansatz revealed large discrepancies between calculated () and found [M]_D-values. Possible reasons for this failure are discussed.

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61. Mitt. über Ferrocenderivate

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39. Mitt.:A. Meyer, H. Neudeck undK. Schlögl, Chem. Ber.110, 1403 (1977).

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60. Mitt.:V. Rapi, K. Schlögl undB. Steinitz, J. Organometal. Chem.94, 87 (1975).     

A Safe Way of Performing Some Dangerous Experiments. II. Construction of a Safety Dropper

Due to the high safety risks, chemistry instructors avoid demonstrating many remarkable experiments based on the addition of a liquid to a solid. Well-known examples of such demonstrations are various pyrotechnic mixtures of potassium chlorate and sugar (sucrose), which are usually activated with a drop of concentrated sulfuric acid. Other attractive demonstrations are the addition of water to freshly prepared magnesium phosphide and addition of water to burning magnesium. In all of these demonstrations the reaction that takes place immediately is very vigorous and can be hazardous for the instructor. Because chemistry teachers and instructors usually try to avoid performing experiments that include a hazard, a number of highly attractive experiments may remain unknown to the public. Using a simple homemade device called a safety dropper, one can perform all of these experiments with complete safety, both for the audience and the demonstrator. Details for performing some of these experiments as well as for the construction of the safety dropper are given in this paper. Video clips of demonstrations are included as an aid for inexperienced instructors.     

Radiation-induced polymerization of cyclohexene sulfide in the solid state

Radiation-induced solid-state polymerization of cyclohexene sulfide has been investigated. Differential thermal analysis shows that this compound has a phase transition point at ?74°C and behaves as a plastic crystal in the temperature range from ?74 to ?20°C (melting point). By rapid cooling, this plastic crystal was easily supercooled, and below ?166°C a glassy crystal, i.e., a supercooled nonequilibrium state of plastic crystal, was obtained. In-source polymerization proceeded in the plastic crystalline state. Postpolymerization of glassy crystalline monomer irradiated at ?196°C occurred above ?166°C (glass transition point) during subsequent heating.     

Mechanism of the cyclization of dimethyl diethynyl silane with selenium tetrabromide: Computational and structural studies, and monitoring

The structure of 2,4-dibromo-2-dibromomethyl-3,3-dimethyl-1-selena-3-silacyclopentene-4, formed by regioselective electrophilic addition of SeBr₄ to dimethyl diethynyl silane, has been determined using X-ray analysis technique. Quantum chemistry methods were used to study elementary stages of the reaction. It was found that the first stage consisted of SeBr₄ conversion into bimolecular complex Br₂?SeBr₂, initiated by dimethyl diethynyl silane. Possible formation of five-membered and six-membered heterocycles involves different cyclization mechanisms. The formation of only five-membered heterocycle is explained by kinetically preferable ring closure through four-center transition state. The conclusions obtained by calculations were confirmed by monitoring of the reaction using ¹H NMR method.