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

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

An equilibrium model for RFP plasmas in the presence of resonant tearing modes

The equilibrium of a finite-beta RFP plasma in the presence of saturated-amplitude tearing modes is investigated. The singularities of the MHD force balance equation JXB=grad(p) at the modes rational surfaces are resolved through a proper regularization of the zeroth-order (equilibrium) profiles, by setting to zero there the gradient of the pressure and parallel current density. An equilibrium model, which satisfies the regularization rule at the various rational surfaces, is developed. The comparison with the experimental data from the Reversed Field eXperiment (RFX) gives encouraging results. The model provides an easy tool for magnetic analysis: many aspects of the perturbations can be analyzed and reconstructed.Comment: Final accepted version. 36 page

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

Применение марковских процессов для анализа и управления эксплуатационной технологичностью летательного аппарата

The process of aircraft operation involves constant effects of various factors on its components leading to accidental or systematic changes in their technical condition. Markov processes are a particular case of stochastic processes, which take place during aeronautical equipment operation. The relationship of the reliability characteristics with the cost recovery of the objects allows us to apply the analytic apparatus of Markov processes for the analysis and optimization of maintainability factors. The article describes two methods of the analysis and control of object maintainability based on stationary and non-stationary Markov chains. The model of a stationary Markov chain is used for the equipment with constant in time intensity of the events. For the objects with time-varying events intensity, a non-stationary Markov chain is used. In order to reduce the number of the mathematical operations for the analysis of aeronautical engineering maintainability by using non-stationary Markov processes an algorithm for their optimization is presented. The suggested methods of the analysis by means of Markov chains allow to execute comparative assessments of expected maintenance and repair costs for one or several one-type objects taking into account their original conditions and operation time. The process of maintainability control using Markov chains includes search of the optimal strategy of maintenance and repair considering each state of an object under which maintenance costs will be minimal. The given approbation of the analysis methods and maintainability control using Markov processes for an object under control allowed to build a predictive-controlled model in which the expected costs for its maintenance and repair are calculated as well as the required number of spare parts for each specified operating time interval. The possibility of using the mathematical apparatus of Markov processes for a large number of objects with different reliability factors distribution is shown. The software implementation of the described methods as well as the usage of tabular adapted software will contribute to reducing the complexity of the calculations and improving data visualization.Процесс эксплуатации летательного аппарата сопровождается постоянным воздействием различных факторов на его компоненты, приводящие к случайным или систематическим изменениям их технического состояния. Марковские процессы являются частным случаем случайных процессов, которые имеют место в процессе эксплуатации объектов авиационной техники. Очевидная связь характеристик безотказности объектов с затратами на их восстановление позволяют применить аналитический аппарат марковских процессов для анализа и управления эксплуатационной технологичностью летательных аппаратов. В статье описываются методы анализа и управления эксплуатационной технологичностью объектов, основанных на стационарных и нестационарных марковских цепях. Модель стационарной марковской цепи используется для объектов, у которых интенсивность событий постоянна во времени. Для объектов с переменной во времени интенсивностью событий используется нестационарная марковская цепь. С целью сокращения вычислительных объемов, необходимых для выполнения анализа эксплуатационной технологичности объектов авиационной техники с помощью нестационарных марковских процессов, представлен алгоритм их оптимизации. Предложенные методы анализа с помощью марковских цепей позволяют провести сравнительные оценки ожидаемых затрат на техническое обслуживание и ремонт одного или нескольких однотипных объектов с учётом их начальных состояний и времени эксплуатации. Процесс управления эксплуатационной технологичностью с использованием марковских цепей заключается в поиске оптимальной при каждом состоянии объекта стратегии технического обслуживания и ремонта (варианта действий), при которой затраты на его техническую эксплуатацию будут минимальными. Проведённая апробация методов анализа и управления эксплуатационной технологичностью с использованием марковских процессов для объекта, подконтрольного в эксплуатации, позволила построить прогнозно-управляемую модель, в которой рассчитаны ожидаемые затраты на его техническое обслуживание и ремонт, а также необходимое количество запасных частей на каждый заданный интервал наработки. Показана возможность использования математического аппарата марковских процессов для большого количества объектов с различными законами распределения характеристик надёжности. Программная реализация описанных методов, а также использование программного обеспечения, адаптированного к табличной среде, будут способствовать снижению трудоёмкости расчётов и более наглядному представлению получаемых данных

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

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

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

Adiabatic theory of Wannier threshold laws and ionization cross sections

The Wannier threshold law for three-particle fragmentation is reviewed. By integrating the Schroedinger equation along a path where the reaction coordinate R is complex, anharmonic corrections to the simple power law are obtained. These corrections are found to be non-analytic in the energy E, in contrast to the expected analytic dependence upon E