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

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

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

Einfluss der Oberflächenbeschaffenheit auf die Intensivierung des Siedens von Kältemitteln

Aufgrund der durchgeführten Untersuchung kann man folgende Schlußfolgerungen ziehen: Verändert man die Art der Wärmeübergangsfläche, kann man eine Zunahme der Wärme-übergangszahl um das 5 – 7fache erreichen. Kältemittel mit stark ausgeprägten wärmephysikalischen Eigenschaften wie R22 und Ammoniak verlangen ein spezielles Vorgehen bei der Auswahl der effektiven Wärmeüber-gangsfläche. Die untersuchten Rohre mit porösem aufgedampftem Belag intensivieren den Siede-vorgang von Ammoniak nur schwach. Dafür bräuchte man Rohre mit anderen geo-metrischen Werten der Beläge. Es muß also weiter untersucht werden, wie Werkstoff des Belags und Standzeit der Oberfläche den Wärmeübergang beeinflussen

Non-Hermitian matrix description of the PT symmetric anharmonic oscillators

Schroedinger equation H \psi=E \psi with PT - symmetric differential operator H=H(x) = p^2 + a x^4 + i \beta x^3 +c x^2+i \delta x = H^*(-x) on L_2(-\infty,\infty) is re-arranged as a linear algebraic diagonalization at a>0. The proof of this non-variational construction is given. Our Taylor series form of \psi complements and completes the recent terminating solutions as obtained for certain couplings \delta at the less common negative a.Comment: 18 pages, latex, no figures, thoroughly revised (incl. title), J. Phys. A: Math. Gen., to appea

Predictive Models for the Free Energy of Hydrogen Bonded Complexes with Single and Cooperative Hydrogen Bonds

© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, WeinheimIn this work, we report QSPR modeling of the free energy ΔG of 1 : 1 hydrogen bond complexes of different H-bond acceptors and donors. The modeling was performed on a large and structurally diverse set of 3373 complexes featuring a single hydrogen bond, for which ΔG was measured at 298 K in CCl4. The models were prepared using Support Vector Machine and Multiple Linear Regression, with ISIDA fragment descriptors. The marked atoms strategy was applied at fragmentation stage, in order to capture the location of H-bond donor and acceptor centers. Different strategies of model validation have been suggested, including the targeted omission of individual H-bond acceptors and donors from the training set, in order to check whether the predictive ability of the model is not limited to the interpolation of H-bond strength between two already encountered partners. Successfully cross-validating individual models were combined into a consensus model, and challenged to predict external test sets of 629 and 12 complexes, in which donor and acceptor formed single and cooperative H-bonds, respectively. In all cases, SVM models outperform MLR. The SVM consensus model performs well both in 3-fold cross-validation (RMSE=1.50 kJ/mol), and on the external test sets containing complexes with single (RMSE=3.20 kJ/mol) and cooperative H-bonds (RMSE=1.63 kJ/mol)

Calculation of the properties of the rotational bands of 155,157^{155,157}Gd

We reexamine the long-standing problem of the microscopic derivation of a particle-core coupling model. We base our research on the Klein-Kerman approach, as amended by D\"onau and Frauendorf. We describe the formalism to calculate energy spectra and transition strengths in some detail. We apply our formalism to the rotational nuclei $^{155,157}$Gd, where recent experimental data requires an explanation. We find no clear evidence of a need for Coriolis attenuation.Comment: 27 pages, 13 uuencoded postscript figures. Uses epsf.st

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