Probability relations involving several subsystems

We consider the question of factorizability in tensor product spaces, and argue that the correlations associated with entangled states are even more problematic in the general case involving any tensor product of Hilbert spaces, than in the Einstein, Podolsky, and Rosen case with only two [1].     

A Law of Large Numbers for the Zeroes of Heine–Stieltjes Polynomials

We determine the limiting density of the zeroes of Heine–Stieltjes polynomials (or of any set of points satisfying the conclusion of Heine–Stieltjes Theorem) in the thermodynamic limit and use this to prove a strong law of large numbers for the zeroes.     

相互作用对玻色气体热力学性质及稳定性的影响

根据由赝势法得到的非理想玻色气体的自由能和状态方程，研究了相互作用对凝聚温度的影响.从热力学角度揭示了存在引力作用时定压热容量、等温压缩系数、定压膨胀系数的反常热力学特性.研究了引力作用下玻色气体系统的不稳定性，给出了不稳定性的温度判据和粒子数密度判据. 关键词： 相互作用 玻色气体 热力学性质 不稳定性判据     

Deuteron electromagnetic form factors and tensor polarization observables in the framework of the hard-wall AdS/QCD model

We study the electromagnetic form factors and tensor polarization observables of the deuteron in the framework of the hard-wall AdS/QCD model. We find a profile function for the bulk twist \begin{document}$\tau=6$\end{document} vector field, which describes the deuteron on the boundary and fix the infrared boundary cut-off of AdS space in accordance with the ground state mass of the deuteron. We obtain the deuteron charge monopole, quadrupole, and magnetic dipole form factors and tensor polarization observables from the bulk Lagrangians for the deuteron and photon field interactions. We plot the momentum transfer dependence of the form factors and tensor polarization observables and compare our numerical results with those in the soft-wall model and experimental data.     

Zum chemischen Transport von Molybdän mit SbBr3 – Experimente und Modellrechnungen

On the Chemical Transport of Molybdenum using SbBr₃ – Experiments and Thermochemical Calculations Mo migrates in a temperature gradient from the region of higher temperature to the lower temperature using SbBr₃ as transport agent. For various mean transport temperatures (750 ? T ? 1000°C; T = 0,5 (T₁ + T₂); T₂ ? T₁ = 100°C) we observed small transport rates (? ? 0,6 mg/h) which rise up to 16 mg/h for higher transport agent concentrations. Small amounts of MoO₂ and Sb were detected beside Mo in the sink. The observed solid phases in the sink are in agreement with thermodynamical calculations by CVTrans which also demonstrate that the formation of MoO₂ and Sb as well as the transport effect of SbBr₃ are caused by traces of H₂O from the quartz glass wall. The sequence of deposition of Mo, MoO₂ and Sb in the examined temperature range can be calculated (CVTrans) and measured with the transport balance.     

Zum chemischen Transport von SiAs mit Iod — Experimente und Modellrechnungen

On the Chemical Transport of SiAs using Iodine — Experiments and Thermochemical Calculations Using iodine as transport agent siliconarsenide migrates in a temperature gradient. The direction of the migration depends on the chosen temperature and the concentration of the transport agent. The transport rates were measured for various transport agent concentrations (0.0002 ? C(I₂) ≥ 0,02 mmol/cm³) and for various mean transport temperatures (650 ? T? ? 1 000°C). For low temperatures (e.g. T₁ = 750°C→T₂ = 850°C), low iodine concentrations (e.g. C(I₂) = 0.001 mmol/cm³) and in the presence of H₂O (from wall of silica ampoule) the following exothermic reaction is responsible for the deposition of SiAs-crystals in the sink region:

• SiAs_s + 4HI_g = SiI_4,g + 2H_2,g + 1/4As_4,g

In case of higher temperatures (e.g. T₂ = 1 050°C→T₁ = 950°C) and higher iodine concentrations (e.g. C(I₂) = 0.02 mmol/cm³) SiI_4,g is the transport agent. According to model calculations the following endothermic reaction is responsible for the migration of SiAs to the region of the lower temperature:

• SiAs_s + SiI_4,g = 2SiI_2,g + 1/4As_4,g

The heterogeneous and homogenous equilibria will be discussed and an explanation of the non equilibrium transport behaviour of SiAs is given. Thermochemical data of SiAs are characterized by the quartzmembrane zero manometer technique and further verified by model calculations.     

Model-independent constraints on spin observables

We discuss model-independent constraints on spin observables in exclusive and inclusive reactions, with special attention to the case of photoproduction.     

On Fuzzy Probability Theory

Our main aim from this work is to see which theorems in classical probability theory are still valid in fuzzy probability theory. Following Gudder's approach [Demonestratio Mathematica 31(3), 1998, 235–254; Foundations of Physics, 30, 1663–1678] to fuzzy probability theory, the basic concepts of the theory, that is of fuzzy probability measures and fuzzy random variables (observables), are presented. We show that fuzzy random variables extend the usual ones. Moreover, we prove that for any separable metrizable space, the crisp observables coincide with random variables. Then we prove the existence of a joint observable for any collection of observables, and we prove the weak law of large numbers and the central limit theorem in the fuzzy context. We construct a new definition of almost everywhere convergence. After proving that Gudder's definition implies ours and presenting an example that indicates that the converse is not true, we prove the strong law of large numbers according to this definition.     

Linear response and relaxation in quantum lattice systems

For spin-lattice systems, the Kubo formula, expressing the relaxation function in terms of the linear response function, is found to be exact in the thermodynamic limit. In addition, analyticity properties are obtained.