Erratum to: Analysis of the Purcell Effect in the Waveguide Mode by S-Quantization

Optics and Spectroscopy - 10.1134/S0030400X17050095     

Noncommutative Dynamics of Random Operators

We continue our program of unifying general relativity and quantum mechanics in terms of a noncommutative algebra А on a transformation groupoid Γ = E × G where E is the total space of a principal fibre bundle over spacetime, and G a suitable group acting on Γ . We show that every a ∊ А defines a random operator, and we study the dynamics of such operators. In the noncommutative regime, there is no usual time but, on the strength of the Tomita–Takesaki theorem, there exists a one-parameter group of automorphisms of the algebra А which can be used to define a state dependent dynamics; i.e., the pair (А, ϕ), where ϕ is a state on А, is a “dynamic object.” Only if certain additional conditions are satisfied, the Connes–Nikodym–Radon theorem can be applied and the dependence on ϕ disappears. In these cases, the usual unitary quantum mechanical evolution is recovered. We also notice that the same pair (А, ϕ) defines the so-called free probability calculus, as developed by Voiculescu and others, with the state ϕ playing the role of the noncommutative probability measure. This shows that in the noncommutative regime dynamics and probability are unified. This also explains probabilistic properties of the usual quantum mechanics.     

Fundamental Problems in the Unification of Physics

We discuss the following problems, plaguing the present search for the “final theory”: (1) How to find a mathematical structure rich enough to be suitably approximated by the mathematical structures of general relativity and quantum mechanics? (2) How to reconcile nonlocal phenomena of quantum mechanics with time honored causality and reality postulates? (3) Does the collapse of the wave function contain some hints concerning the future quantum gravity theory? (4) It seems that the final theory cannot avoid the problem of dynamics, and consequently the problem of time. What kind of time, if this theory is supposed to be background free? (5) Will the dynamics of the “final theory” be probabilistic? Quantum probability exhibits some essential differences as compared with classical probability; are they but variations of some more general probabilistic measure theory? (6) Do we need a radically new interpretation of quantum mechanics, or rather an entirely new theory of which the present quantum mechanics is an approximation? (7) If the final theory is to be background free, it should provide a mechanism of space-time generation. Should we try to explain not only the generation of space-time, but also the generation of its material content? (8) As far as the existence of the initial singularity is concerned, one usually expects either “yes” or “not” answers from the final theory. However, if the mathematical structure of the future theory is supposed to be truly more general that the mathematical structures of the present general relativity and quantum mechanics, is a “third answer“ possible? Could this third answer be related to the probabilistic character of the final theory? We discuss these questions in the framework of a working model unifying gravity and quanta. The analysis reveals unexpected aspects of these rather wildly discussed issues.     

EPR Studies of Tl0.5Pb0.5Sr1.6Ba0.4CaCu2?xRuxO7?δ Superconductor

Bulk superconducting samples of type Tl_0.5Pb_0.5Sr_1.6Ba_0.4CaCu_2−x Ru _x O_7−δ, (Tl, Pb)/Sr-1212, with 0.0 ≤ x ≤ 0.525 were prepared by the conventional one-step solid-state reaction technique. The prepared samples were investigated using X-ray powder diffraction, electrical resistivity and electron paramagnetic resonance (EPR) measurements. Enhancement of the phase formation, superconducting transition temperature T _c and hole carriers concentration P was observed up to x = 0.075. For x > 0.075, a reverse trend was observed. EPR spectra were measured at different temperatures (120–290 K) for all prepared samples. The number of spins N participating in the resonance and the paramagnetic susceptibility χ were calculated as a function of both Ru-content and temperature. N and χ increased as the Ru-content increased. A linear relationship between logN and 1/T was established, from which the activation energy E _a was calculated as a function of the Ru-content. The temperature dependence of χ was fitted according to Curie–Weiss type of magnetic behavior. Curie constant C, Curie temperature θ, the effective magnetic moment μ and the electronic specific heat γ were estimated as a function of the Ru-content.     

Sheaves of Einstein algebras

To include all types of singularities into a geometrically tractable theoretical scheme we change from Einstein algebras, an algebraic generalization of general relativity, to sheaves of Einstein algebras. The theory of such spaces, called Einstein structured spaces, is developed. Both quasiregular and curvature singularities are studied in some detail. Examples of the closed Friedmann world model and the Schwarzschild spacetime show that Schmidt'sb-boundary is a useful theoretical tool when considered in the category of structured spaces.     

Tamm plasmon-polaritons: First experimental observation

We report on the first experimental observation of Tamm plasmon-polaritons (TPP) formed at the interface between a metal and a dielectric Bragg reflector (DBR). Contrary to conventional surface plasmons, TPPs have an in-plane wave vector less than the wave vector of light in vacuum, which allows for their direct optical excitation, and can be formed in both the TE and TM polarizations. The angular resolved reflectivity and transmission spectra of a GaAs/AlAs DBR covered by Au films of various thicknesses show the resonances associated with the TPP at low temperatures and at room temperature. The in-plane dispersion of TTPs is parabolic with an effective mass 4×10⁻⁵$4\times 10^{-5}$ of the free electron mass.     

Effect of IR laser radiation on the structure and optical properties of PC-PBT/Pd polymer nanocomposite films

ABSTRACT

Bayfol (PC-PBT blend ?lm) is a class of polymeric solid-state nuclear track detector which has a lot of applications in several radiation detection ?elds. It is a bisphenol-A polycarbonate PC blended with polybutylene terephthalate PBT. Bayfol/Palladium (PC-PBT/Pd) nanocomposite films have been deposited using the molding technique. It is worth mentioning that this report is almost the first one dealing with the topic of the changes of physical properties of Bayfol/Pd nanocomposite due to laser exposure. Samples from PC-PBT/Pd (5?wt%) nanocomposite were exposed to IR-pulsed laser of 5-W power, capable of producing 2000 pulses per second with pulse duration of 200?ns at 904?nm. The laser fluences were in the range 2–25?J/cm². The resultant modi?cations in the exposed nanocomposite samples have been studied as a function of fluence using different characterization techniques such as X-ray diffraction (XRD), UV spectroscopy and color difference studies. The results indicate the proper dispersion of Pd nanoparticles in the PC-PBT matrix that causes a strong intermolecular interaction between Pd and PC-PBT, resulted in an increase in refractive index and the amorphous phase. Also, it is found that the laser exposure reduces the optical energy gap that could be attributed to the increase in structural disorder of the exposed PC-PBT/Pd nanocomposites due to crosslinking. Further, the color intensity ΔE, which is the color difference between the exposed samples and the non-exposed one, was increased with increasing the laser fluence, convoyed by a significant increase in the green and yellow color components.     

昆虫信息素研究III: 拟蚜虫警戒素的研究

合成了一系列碳数为十五和十四的倍半萜类蚜虫警戒素,并进行了生物活性测定,从中筛选有效化合物.