Grassmann-Cartan algebra and Klein-Gordon equations

Given a Riemannian structure (M, g), a hypothesis is investigated that if= _p=0 ⁿ _p (M) is submitted to the differential condition (g++)=0, =mc/—which implies that each component of fulfills the Klein-Gordon equation (- ²) _p =0, ought to be interpreted as a natural complex of the bosonic fields. Then it is found that the complex admits the interpretation in the sense of first quantization with (M) being a convex set of states, with the structure of a Hilbert space over . The definite spin states of bosons are then pure states which are not conserved by the temporal evolution.     

Quantum Observables,Lie Algebra Homology and TQFT

Let us consider a Lie (super)algebra G spanned by T where T are quantum observables in BV formalism. It is proved that for every tensor c^... that determines a homology class of the Lie algebra G the expression c^...T...T is again a quantum observable. This theorem is used to construct quantum observables in the BV sigma model. We apply this construction to explain Kontsevich's results about the relation between homology of the Lie algebra of Hamiltonian vector fields and topological invariants of manifolds.     

A new approach to the problem of the anomalous magnetic moment of the electron

A heuristic model for deriving the anomalous magnetic moment of the electron is presented. A term /2 – 0.327(/)² is deduced, in better agreement with experiment than is the QED derivation of /2 – 0.328(/)². The result is strengthened by the recent non-QED account of the Lamb shift by Yu and Sachs.     

The Einstein 3-form Gα and its Equivalent 1-form Lα in Riemann–Cartan Space

We motivate the definition of the Einstein 3-form G by means of the contracted 2nd Bianchi identity. This definition contains the whole curvature 2-form. The L 1-form, defined via G = L ^*( ) ( is the Hodge-star, the coframe), is equivalent to the Einstein 3-form and contains all the information of the curvature 2-form relevant for the definition of the Einstein 3-form. A variational formula of Salgado on quadratic invariants of the L 1-form is discussed, generalized, and put into proper perspective.     

Defect annealing of alpha-particle irradiated n-GaAs

The annealing behaviour of irradiation induced defects in n-type GaAs irradiated at 300 K with 5.4 MeV alpha-particles from an americium-241 (Am-241) radio nuclide have been investigated. The annealing kinetics are presented for the alpha-particle induced defects E1–E5 detected in Organo-Metallic Vapor Phase Epitaxially (OMVPE) grown n-GaAs doped with silicon to 1.2×10¹⁶ cm^–3, these kinetics are compared to those obtained for similar defects (E1–E5) detected after electron irradiation. While defects P1 and P2 were detected after removal of the electron defects E4 and E5, respectively, a new defect labelled P0, located 0.152 eV below the conduction band, was introduced by annealing. The thermal behaviour and trap characteristics of these three defects (P0–P2) are presented. In an attempt to further characterise defects P0 and P1 a preiliminary study investigating the emission rate field dependence of these defects was conducted, it was observed that defect P0 exhibited a fairly strong field dependence while P1 exhibited a much weaker dependence.     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

Statistics of the One-Dimensional Riemann Walk

The Riemann walk is the lattice version of the Lévy flight. For the one-dimensional Riemann walk of Lévy exponent 0<<2 we study the statistics of the support, i.e., set of visited sites, after t steps. We consider a wide class of support related observables M(t), including the number S(t) of visited sites and the number I(t) of sequences of adjacent visited sites. For t we obtain the asymptotic power laws for the averages, variances, and correlations of these observables. Logarithmic correction factors appear for =2/3 and =1. Bulk and surface observables have different power laws for 1<2. Fluctuations are shown to be universal for 2/3 <2. This means that in the limit t the deviations from average M(t)M(t)–M-0304;(t-0304;) are fully described either by a single M independent stochastic process (when 2/3 <1) or by two such processes, one for the bulk and one for the surface observables (when 1<<2).     

Low-temperature and long-time anomalies of a damped quantum particle

The time evolution of a damped quantum particle is discussed. Dissipation is modeled by the bilinear coupling to a set of harmonic oscillators. Using a functional integral technique that accounts for initial correlations between the particle and the reservoir, one can express the dynamics of the damped particle entirely in terms of equilibrium correlation functions. The long-time behavior of these correlations is determined for memory damping arising from the coupling to a reservoir with spectral densityI() at low frequencies, where > 0. The time evolution of nonequilibrium initial states of the damped particle is discussed. At finite temperatures an initially localized state is found to spread subdiffusively or superdiffusively, depending on . For > 2 the damping becomes ineffective for long times, and the width of a state grows kinematically. At zero temperature and for < 1, an initially localized state remains localized for all times. For 1 the state spreads, but with a slower rate than at finite temperatures. Study of arbitrary initial states indicates that the process is ergodic at finite temperatures only for 2 and at zero temperature for 1 2.     

What determinates the chemical changes of the internal conversion coefficients for inner atomic shells?

Calculations of internal conversion coefficients (ICC) of the E1–E4 and M1–M4 transitions for nuclei in ions show that the relative changes _i / _i of the ICC _i for deep inner subshells can differ significantly from the relative changes _i/_i of the electron densities _i at the nucleus. For the K conversion _i/ _i are many times greater than _i/_i. Especially large deviations of _i/ _i are characteristic of transitions of high multipolarity; however, for the M1 transitions they can also be significant. Illustrations of various dependencies of _i/ _iare presented for the conversion in the regionZ-50.     

On P-representation for parametric amplifier and parametric frequency converter

The statistical properties of a parametric amplifier and a frequency converter are studied by means of quantum mechanical methods. The Schrödinger picture and the P-representation of the density matrix are used. Carrying out the Fourier transformation of the Liouville equation a partial differential equation for a generating function is obtained. The inverse Fourier transform of a solution of this equation is a time-dependent P-representationPN( ₁, ₂,t). For the parametric amplifier a relation is derived which enables us to compute the functionPA( ₁, ₂,t) = =1< ₁, ₂/ ₁> is shown thatPA is classical distribution ifPN( ₁, ₂,0) is a positive distribution, while the P-representationPN( ₁, ₂,t) need not exist as a distribution and the P-representationPN( ₁, ₂,t) for the parametric frequency converter is constant along classical trajectories.The author wishes to thank Dr. J. Peina for stimulating discussions.     

Double hypernuclei and the Λ-Λ interaction

The binding energy of the double hypernucleus Be¹⁰ analyzed using an -particle model. A relationship is found between B, the binding energy of two -particlcs, and ¯V, the - potential integral. For the experimental value B = 17.5 Me V ¯V varies from 250 to 850 MeV-F³ according to the form of the - potential used.In conclusion, I wish to thank S. N. Kryuchkova for carrying out these calculations on a Minsk-2 electronic computer. I also wish to thank my senior colleague, V. A. Filimonov, for his support in the completion of the present work.     

A theory of 1/f noise

Letu() be an absolutely integrable function and define the random process where thet _i are Poisson arrivals and thes _i, are identically distributed nonnegative random variables. Under routine independence assumptions, one may then calculate a formula for the spectrum ofn(t), S _n(), in terms of the probability density ofs, p_s(). If any probability density p_s() having the property p_s() I for small is substituted into this formula, the calculated S_n() is such that S_n() 1 for small . However, this is not a spectrum of a well-defined random process; here, it is termed alimit spectrum. If a probability density having the property p_s() for small , where > 0, is substituted into the formula instead, a spectrum is calculated which is indeed the spectrum of a well-defined random process. Also, if the latter p_s is suitably close to the former p_s, then the spectrum in the second case approximates, to an arbitrary, degree of accuracy, the limit spectrum. It is shown how one may thereby have 1/f noise with low-frequency turnover, and also strict 1/f ^1– noise (the latter spectrum being integrable for > 0). Suitable examples are given. Actually, u() may be itself a random process, and the theory is developed on this basis.     

Lattice vibrations in ordered and disordered thiourea

The critical dynamics of the Syozi model for dilute ferromagnetism is considered by the use of master equations. The dynamics is soluble as it is assumed that the time scale of motion on the sublattice on which the impurities move is so much faster than on the other sublattice that fast relaxing variables may be adiabatically eliminated, leaving a new soluble master equation. It is found that the linear and non-linear relaxation of magnetization exponents ^(l) and ^(nl) increase on dilution to ^(l)/(1–) and ^(nl)/(1–) respectively ( is the specific heat exponent for the pure system, which itself changes on dilution to –/(1–)). Thus if the exponents for the pure system obey the scaling law of Rácz and Fisher ^(nl)= ^(l)– ( is the magnetization exponent which changes on dilution to /(1–)) then so do the exponents for the diluted system. Similarly the exponent for spin diffusion changes on dilution to /(1–).     

Solution of coupled differential equations of soliton theory

We present the complete set of solutions of the coupled differential equations of the form ()²=(), ² =(). Equations of this form appear in several physical situations.     

On the existence of invariant,absolutely continuous measures

Let (, , ) be a measure space with normalized measure,f: a nonsingular transformation. We prove: there exists anf-invariant normalized measure which is absolutely continuous with respect to if and only if there exist >0, and , 0<<1, such that (E)< implies (f ^–k(E))< for allk0.     

Vacuum Einstein spaces with axial symmetry

Four classes of solutions are found to the equations R=–2_{; ;} and g _;=0 in three-dimensional space with metric gdxdx and signature (+ ––), equivalent to the Einstein equations R_ij=0 in a vacuum for the metric . The metric ds² assumes axial symmetry and symmetry with respect to the reflection .Translated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 9, pp. 43–45, September, 1976.     

Upper bounds onT c for one-dimensional Ising systems

We present upper bounds on the critical temperature of one-dimensional Ising models with long-range,l/n interactions, where 1<2. In particular for the often studied case of =2 we have an upper bound onT _c which is less than theT _c found by a number of approximation techniques. Also for the case where is small, such as =1.1, we obtain rigorous bounds which are extremely close, within 1.0%, to those found by approximation methods.     

A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants

We study ergodic Jacobi matrices onl ²(Z), and prove a general theorem relating their a.c. spectrum to the spectra of periodic Jacobi matrices, that are obtained by cutting finite pieces from the ergodic potential and then repeating them. We apply this theorem to the almost Mathieu operator: (H _{, ,} u)(n)=u(n+1)+u(n–1)+ cos(2n+)u(n), and prove the existence of a.c. spectrum for sufficiently small , all irrational 's, and a.e. . Moreover, for 0<2 and (Lebesgue) a.e. pair , , we prove the explicit equality of measures: |_ac|=||=4 –2.Work partially supported by the US-Israel BSF     

Some results for the exponential interaction in two or more dimensions

We show that for the regularized exponential interaction :e : ind space-time dimensions the Schwinger functions converge to the Schwinger functions for the free field ifd>2 for all or ifd=2 for all such that ||>₀.Partially sponsored by the I.H.E.S. through the Stiftung Volkswagenwerk