PCT, spin and statistics, and analytic wave front set

A new, more general derivation of the spin-statistics and PCT theorems is presented. It uses the notion of the analytic wave front set of (ultra)distributions and, in contrast to the usual approach, covers nonlocal quantum fields. The fields are defined as generalized functions with test functions of compact support in momentum space. The vacuum expectation values are thereby admitted to be arbitrarily singular in their space-time dependence. The local commutativity condition is replaced by an asymptotic commutativity condition, which develops generalizations of the microcausality axiom previously proposed.Comment: LaTeX, 23 pages, no figures. This version is identical to the original published paper, but with corrected typos and slight improvements in the exposition. The proof of Theorem 5 stated in the paper has been published in J. Math. Phys. 45 (2004) 1944-195

Разработка алгоритмов выделения и систематизации отсчётов составляющих вторичной модуляции

The objective of this work was to develop the algorithm for selection of secondary modulation samples and their subsequent systematization. These algorithms are needed to resolve the ambiguity of definition of frequency modulation and measure its dependence on time. Processing the real data of centimeter-band SOU BUC-M1 radar shows the result of used algorithm.The secondary modulation effect of the centimeter waves - irradiated airplane generates a set of components. The fact that the pulse repetition rate is significantly lower than the frequency modulation leads to aliasing, which is the reason of ambiguity.A serious problem in the selection of the modulation components is the presence of side lobes. Therefore, the algorithm must assume their selection. The component form is determined by sinc function, with all components being of the same width. Selecting the modulation components is a procedure of search for a local maximum signal and measuring its sinc parameters (offset and amplitude). Measurement of parameters is realized by solving a system of nonlinear equations. The selection of the side lobes is realized by comparing the residual solutions of equations with a threshold. The residual for the modulation components tend to zero, and for the side lobe is great.Ambiguity of measuring component frequency can be overcome by measuring the frequency of the chirp pulse duration. Uniqueness in this case is determined by the sampling frequency, which is quite large and includes the entire spectrum of components of secondary modulation. The problem is that the measuring, in this way, frequency error is very high, it exceeds the pulse repetition rate.The way out of this situation is the algorithm of ordering samples to select the components of modulation, which are caused by the same modulation frequency, and to assign their appropriate harmonic number. Thus, an unambiguous measurement of the frequency modulation and components it made. Combination of samples in time is realized by sampling frequency modulation.Работа посвящена вопросам обработки радиолокационного сигнала, отраженного от аэродинамических целей с наличием эффекта вторичной модуляции. Рассматривается обнаружение составляющей модуляции в нескольких смежных каналах обработки. Разработан алгоритм преобразования этой информации в один вектор параметров, характеризующих данную составляющую модуляции. Также разработан алгоритм, позволяющий выделить составляющие вторичной модуляции по критерию принадлежности к той или иной частоте модуляции DOI: 10.7463/rdopt.0515.077798

Experimentelle Untersuchung des Wärmeübergangs beim Sieden von R 22 und R 717 an verschiedenartigen Oberflächen in horizontalen Rohrbündelverdampfern

Beschrieben werden die Ergebnisse der experimentellen Untersuchungen des Wärmeübergangs beim Sieden von Kältemitteln an horizontalen Rohren mit verschiedenartigen Oberflächen. Die Heizwirkung der untersuchten Oberflächen wird verglichen. Desweiteren werden die Ergebnisse von Versuchen beschrieben, die sich mit den Verwendungseigenschaften der Wärmeübergangsflächen befassen: Hystereseerscheinungen im Bereich des nicht ausgebildeten Siedens; Einfluß glatter, untereinander angeordneter Rohre; Einfluß eines Horizontal-rohrbündels auf den Wärmeübergang einzeln ausgewählter Rohre in einer jeden waagrechten Reihe. Angegeben werden die Versuchsdaten, bei denen eine starke Zunahme (um mehr als das 2fache) auf die Wärmeübergangskoeffizienten in den oberen Reihen von Glattrohrbündeln festgestellt wurde, verglichen mit den unteren Reihen. Es wird nachgewiesen, daß der Intensivierungsgrad des Wärmeübergangs nach Aufbringen einer porösen Schicht mit zunehmender Anzahl horizontaler Rohrreihen im Bündel abnimmt

Long quasi-periodic oscillations of the faculae and pores

Aims. The main goal of this work is to analyze the structural and temporal evolution of small-scale magnetic structures (SSMSs) observed in the solar atmosphere, such as solitary faculae and pores, and reveal long quasi-periodic oscillations of these structures.Methods. The statistical method of regression analysis and the wavelet transform were used to obtain the periods of oscillations and dependences between the parameters of magnetic structures and periods of oscillations.Results. Long-period oscillations with periods in the interval of 18-260 min are found for the structurally stable phase of SSMSs at the level of the solar photosphere. These long-period oscillations were interpreted as natural oscillations of the structurally stable long-lived magnetic structures around their equilibrium position. These oscillations, which are of similar nature, are observed in the chromospheric bright formations associated with photospheric SSMSs. Dependences between the magnetic field and the continuum intensity of the facula elements were found. It is shown that the continuum intensity of a SSMS decreases when its magnetic field increases

Magnetohydrodynamic equilibria of a cylindrical plasma with poloidal mass flow and arbitrary cross section shape

The equilibrium of a cylindrical plasma with purely poloidal mass flow and cross section of arbitrary shape is investigated within the framework of the ideal MHD theory. For the system under consideration it is shown that only incompressible flows are possible and, conscequently, the general two dimensional flow equilibrium equations reduce to a single second-order quasilinear partial differential equation for the poloidal magnetic flux function $\psi$, in which four profile functionals of $\psi$ appear. Apart from a singularity occuring when the modulus of Mach number associated with the Alfv\'en velocity for the poloidal magnetic field is unity, this equation is always elliptic and permits the construction of several classes of analytic solutions. Specific exact equlibria for a plasma confined within a perfectly conducting circular cylindrical boundary and having i) a flat current density and ii) a peaked current density are obtained and studied.Comment: Accepted to Plasma Physics & Controlled Fusion, 14 pages, revte

Ionization of hydrogen and hydrogenic ions by antiprotons

Presented here is a description of the ionization of hydrogen and hydrogenic ions by antiproton-impact, based on very large scale numerical solutions of the time-dependent Schr\"odinger equation in three spatial dimensions and on analysis of the topology of the electronic eigenenergy surfaces in the plane of complex internuclear distance. Comparison is made with other theories and very recent measurements.Comment: RevTex document, 11 pages, 4 Postscript figures are available from the authors, in press Phys. Rev. Let

Hydrogen atom in crossed external fields reexemined by the moment method

Recurrence relations of perturbation theory for hydrogen ground state are obtained. With their aid polarizabilities in constant perpendicular electric and magnetic fields are computed up to 80th order. The high orders asymptotic is compared with its quasiclassical estimate. For the case of arbitrary mutual orientation of external fields a general sixth order formula is given.Comment: 11 pages, LaTeX, 2 figures (eps

Projective Hilbert space structures at exceptional points

A non-Hermitian complex symmetric 2x2 matrix toy model is used to study projective Hilbert space structures in the vicinity of exceptional points (EPs). The bi-orthogonal eigenvectors of a diagonalizable matrix are Puiseux-expanded in terms of the root vectors at the EP. It is shown that the apparent contradiction between the two incompatible normalization conditions with finite and singular behavior in the EP-limit can be resolved by projectively extending the original Hilbert space. The complementary normalization conditions correspond then to two different affine charts of this enlarged projective Hilbert space. Geometric phase and phase jump behavior are analyzed and the usefulness of the phase rigidity as measure for the distance to EP configurations is demonstrated. Finally, EP-related aspects of PT-symmetrically extended Quantum Mechanics are discussed and a conjecture concerning the quantum brachistochrone problem is formulated.Comment: 20 pages; discussion extended, refs added; bug correcte

Magneto-intersubband oscillations in two-dimensional systems with an energy spectrum split due to spin-orbit interaction

In the present paper we study magneto-intersubband oscillations (MISO) in HgTe/Hg1-xCdxTe single quantum well with "inverted" and "normal" spectra and in In1-xGaxAs/In1-yAlyAs quantum wells with normal band ordering. For all the cases when two branches of the spectrum arise due to spin-orbit splitting, the mutual arrangement of the antinodes of the Shubnikov-de Haas oscillations and the maxima of MISO occurs opposite to that observed in double quantum wells and in wide quantum wells with two subbands occupied and does not agree with the theoretical predictions. A "toy" model is proposed that explains qualitatively this unusual result. © 2020 American Physical Society.We are grateful to A. A. Bykov, I. V. Gornyi, D. G. Polyakov, O. E. Raichev, M. A. Zudov, and V. Ya. Aleshkin for useful discussions. The work has been supported in part by the Russian Foundation for Basic Research (Grant No. 18-02-00050), by Act 211 Government of the Russian Federation (Agreement No. 02.A03.21.0006), by the Ministry of Science and Higher Education of the Russian Federation (Project No. FEUZ-2020-0054), and by the FASO of Russia (theme “Electron” No. 01201463326)