Analyticity properties of eigenfunctions and scattering matrix

For potentialsV=V(x)=O(|x|^–2–) for |x|,x³ we prove that if theS-matrix of (–, –+V) has an analytic extension to a regionO in the lower half-plane, then the family of generalized eigenfunctions of –+V has an analytic extension toO such that for |Imk|<b. Consequently, the resolvent (–+V–z ²)^–1 has an analytic continuation from ⁺ to {kOImk|<b} as an operator from _b ={f=e ^–b|x| g|gL ₂(³)} to _–b . Based on this, we define for potentialsW=o(e ^–2b|x|) resonances of (–+V, –+V+W) as poles of and identify these resonances with poles of the analytically continuedS-matrix of (–+V, –+V+W).The author would like to thank the Institute for Advanced Study for its hospitality and the National Science Foundation for financial support under Grant No. DMS-8610730(1)     

Levi–Civita effect in the polarizable vacuum (PV) representation of general relativity

The polarizable vacuum (PV) representation of general relativity (GR), derived from a model by Dicke and related to the TH formalism used in comparative studies of gravitational theories, provides for a compact derivation of the Levi–Civita effect (both magnetic and electric), herein demonstrated.This revised version was published online in April 2005. The publishing date was inserted.     

Derivation of the Tully—Fisher Law: Doubts About the Necessity and Existence of Halo Dark Matter

For disk galaxies the fourth power of the circular velocity ⁴ _c of stars around thecore of the galaxy is proportional to the luminosity L, ⁴ _c L (Tully—Fisher law).Since L is proportional to the mass M of the galaxy, it follows that ⁴ _c M.Newtonian mechanics, however, yields ² _c = GM/r for a circular motion. In orderto rectify this big difference, astronomers assume the existence of dark matter.We derive the equation of motion of a star moving in the central field of a galaxyand show that, for a circular motion, it yields a term of the form ⁴ _c GMc/,where G is Newton's gravitational constant, c is the speed of light, and is theHubble time. This puts in doubt the existence of halo dark matter for galaxies.     

On the time evolution automorphisms of the CCR-algebra for quantum mechanics

In ordinary quantum mechanics for finite systems, the time evolution induced by Hamiltonians of the form is studied from the point of view of *-automorphisms of the CCRC*-algebra (see Ref. [1, 2]). It is proved that those Hamiltonians do not induce *-automorphisms of this algebra in the cases: a) and b)V L (,dx) L ¹ (,dx), except when the potential is trivial.     

Minimal supersymmetric standard model with the gauge mediated supersymmetry breaking and the neutrinoless double-beta decay

Neutrinoless double-beta decay within Minimal Supersymmetric Standard Model with gauge mediated supersymmetry breaking is considered. Limits on R-parity breaking constant coming from non-observability of 0 in ⁷⁶Ge are found. The dependence of on different parameters at the messenger scale M are shown, with special attention paid to nuclear part of calculations. We have found that strongly depends on the effective supersymmetry breaking scale only and deduced limits imposed on this non-standard parameter by the germanium experiment.     

Scaling characteristics of ac conductivity and dielectric function in fractal regime of the metal-insulator transition

An analysis of the ac conductivity _ac(), and the ac dielectric constant, (), of the metal-insulator percolation systems is presented in the critical regime near the transition threshold. It is argued that the polarization and relaxation of the finite fractal metallic clusters play dominant roles in controlling the dynamic response of the system on both sides of the threshold. The relaxation time constant of a fractal cluster is shown to scale with its size as withd _t = 4 – 2d +d _c + /, whered is tge Euclidean dimension, andd _c , , and are the scaling indices for the charging, the dc conductivity, and the correlation length respectively. The average time dependent response of the system is shown to scale with a new time scale , where is the correlation length and ₀ is a microscopic time constant. It is shown that at frequencies and with /d_t 1, in close agreement with experiments. The effects of the anomalous transport along the infinite cluster and the medium polarizability are also discussed.     

A Quantization on Riemann Surfaces with Projective Structure

Let X be a Riemann surface equipped with a projective structure. Let be a square-root of the holomorphic cotangent bundle K _X . Consider the symplectic form on the complement of the zero section of obtained by pulling back the symplectic form on K _X using the map ². We show that this symplectic form admits a natural quantization. This quantization also gives a quantization of the complement of the zero section in K _X equipped with the natural symplectic form.     

Some results on electronic two- and one photon raman scattering in CdS

Two photon Raman scattering (TPRS) via virtually excited biexcitons is observed in CdS over a rather large spectral region in a scattering configuration which favours stimulated emission. We observe either a pure longitudinal exciton or-for the first time—a bound exciton (I ₂) as final state particles. Furthermore, the anomaly in the relation between _exc and _R at _exc= E_blex is observed for the first time in a II–VI compound, indicating an energy of the ₁ biexciton level of 5.098 eV in agreement with two photon absorption measurements. With an applied magnetic fieldB, the corresponding shift of the exciton eigenenergies can be observed. For the longitudinal exciton, the diamagnetic shift is 0.35 meV atB=10T forBc in agreement with theoretical predictions. In this configuration also a stimulated one photon spin flip Raman scattering is observed, yielding the well known electronicg-value of 1.78.     

New EL2 structural model based on the observation of two sequential photoquenching processes

A generalization of the pure site and pure bond percolation problems in which pairs of nearest neighbor sites (site dimers) and linear pairs of nearest neighbor bonds (bond dimers) are independently occupied at random on a square lattice is studied. We called this model as dimer site-bond percolation. Motivated by considerations of cluster connectivity, we have used two distinct schemes (denoted as and ) for dimer site-bond percolation. In ( ), two points are said to be connected if a sequence of occupied sites and (or) bonds joins them. By using finite-size scaling theory, data from and are analyzed in order to determine i) the phase boundary between the percolating and non-percolating regions and ii) the numerical values of the critical exponents of the phase transition occurring in the system. The results obtained are discussed in comparison with the corresponding ones for classical monomer site-bond percolation.     

Mössbauer effect and discovery of new hexagonal ferrites prepared at 980^\circ C

In the present article, undoped and Codoped Mtype Srhexaferrites have been prepared at low temperatures down to 980 C for the first time by the usual ceramic procedure and sintering technique. On these materials, a CoK Xray diffraction analysis and the room temperature ⁵⁷Fe Mössbauer spectroscopy (MES) were carefully performed. The results obtained are described and interpreted. The mechanism of Co substitution partially in place of iron and the site of its occupancy were proposed and established.     

Cosmology with Curvature-Saturated Gravitational Lagrangian R/\sqrt {1 + l^4 R^2 }

We argue that the Lagrangian for gravity should remain bounded at large curvature, and interpolate between the weak-field tested Einstein-Hilbert Lagrangian _EH = R/16G and a pure cosmological constant for large R with the ansatz _cs = _EH/ , where l is a length parameter expected to be a few orders of magnitude above the Planck length. The curvature-dependent effective gravitational constant defined by d/dR = 1/16G _eff is G _eff = G , and tends to infinity for large R, in contrast to most other approaches where G _eff 0. The theory possesses neither ghosts nor tachyons, but it fails to be linearization stable. In a curvature saturated cosmology, the coordinates with ds ² = a ² [da ²/B(a) – dx ² – dy ² – dz ²] are most convenient since the curvature scalar becomes a linear function of B(a). Cosmological solutions with a singularity of type R ± are possible which have a bounded energy-momentum tensor everywhere; such a behaviour is excluded in Einstein's theory. In synchronized time, the metric is given by

Conformal Transformations as Observables

C denotes either the conformal group in 3+1 dimensions, PSO(4, 2), or in one chiral dimension, PSL(2, ). Let U be a unitary, strongly continuous representation of C satisfying the spectrum condition and inducing, by its adjoint action, automorphisms of a von Neumann algebra . We construct the unique inner representation of the universal covering group of C implementing these automorphisms. satisfies the spectrum condition and acts trivially on any U-invariant vector. This means in particular: Conformal transformations of a field theory having positive energy are weak limit points of local observables. Some immediate implications for chiral subnets are given. We propose the name Borchers–Sugawara construction.     

Duality for free bose fields

An elementary proof of Araki's duality theorem for free fields is presented. The theorem says that for a certain class of regionsO in Minkowski space, the commutant of (O), the von Neumann algebra generated by all observables belonging to measurements withinO, is exactly (O), whereO is the spacelike separated complement ofO.Supported by the National Science Foundation under grants GP 24003, GP 30819X and GP 31239X.     

Chaotic properties of the elliptical stadium

The elliptical stadium is a curve constructed by joining two half-ellipses, with half axesa>1 andb=1, by two straight segments of equal length 2h.Donnay [6] has shown that if 1 <a < and ifh is big enough, then the corresponding billiard map has a positive Lyapunov exponent almost everywhere; moreover,h asa In this work we prove that if , then assures the positiveness of a Lyapunov exponent. And we conclude that, for these values ofa andh, the elliptical stadium billiard mapping is ergodic and has theK-property.During this work, partially supported by Fac. de Ciencias, UruguayPartially supported by CNPq, Brasil     

Slow flow of a conducting fluid past a non-conducting porous sphere with variable permeability

Slow flow of a conducting fluid past a non-conducting porous sphere of variable permeability in presence of a uniform radial magnetic field is studied. The drag experienced by the sphere is shown graphically and compared to that for a non-conducting fluid.Notation velocity vectors of the porous matrix and the conducting fluid - P, p pressures in the porous material and the free fluid - K permeability at a point of the porous medium - viscosity - v (=) kinematic viscosity - magnetic induction - current density - (r, , ) spherical coordinates - dimensionless constant - conductivity of the liquid The authors remain thankful to the referee for his valuable comments and helpful suggestions for improvement of the quality of the paper.     

A limit theorem for stochastic acceleration

We consider the motion of a particle in a weak mean zero random force fieldF, which depends on the position,x(t), and the velocity,v(t)= (t). The equation of motion is (t)=F(x(t),v(t), ), wherex(·) andv(·) take values in ^d ,d3, and ranges over some probability space. We show, under suitable mixing and moment conditions onF, that as 0,v (t)v(t/²) converges weakly to a diffusion Markov processv(t), and ² x (t) converges weakly to , wherex=lim ² x (0).     

The microstructure of electrodeposited amorphous or microcrystalline Fe-P alloys

Dependent on is produced through electrodeposition in three modifications: microcrystalline if , amorphous if and in a mixed state containing both components if . The interpretation of results of large and small angle X-ray scattering, of measurements of the coercivity and of the mechanical density shows that the three modifications consist of two phases. The structure of the grain boundary phase in the microcrystalline alloys differs considerably from that of the amorphous phase. This arises from the dependence of the atomic volume on the average phosphorus content . The volume fraction of the crystalline component decreases with increasing up to . But even in alloys revealing X-ray patterns without any peaks coming from crystalline particles small angle X-ray scattering indicates the existence of metal-rich inclusions occupying some percent of the total volume.     

The quasilinear theory of two-stream cyclotron instability of electron beams

The paper is devoted to a study of cyclotron instability ( _e) of two opposite beams of electrons from the aspect of the quasilinear effects. For this case of instability the authors evolve the diffusion equation in the velocity space for an averaged distribution function. They estimate the relaxation times , _z of the spreading of the distribution function in the velocity space. At the end of the paper, they compare their results with an experiment described by M. Seidl and P. unka [Phys. Letters11 (1964), 31].     

Periodic Motion of Atoms Near a Charged Wire

We study the classical motion of an atom in the vicinity of an infinite straight wire which carries an oscillating uniform charge. This system has been proposed as a mechanism for trapping cold neutral atoms. The parameters of the problem are the magnitude Q and frequency of oscillation of the charge, the mass M and polarizability of the atom, and the angular momentum L of the atom about the wire. For 0 and 2MQ ² greater than, but close to, L ², we prove that the atom's radial motion is periodic (with period 2/), and that the atom moves in a helical path around the wire. For 2MQ ² L ² we prove that the atom must either collide with the wire or else escape to infinity in the radial direction.     

The Heisenberg ferromagnet as a quantum field theory

We consider a lattice of spin 1/2 ions, described by the discrete form of the current commutation relationsJ _i J _(i) =1/2, [J _i ,J _i ]=i _ij J _i where =1, 2, 3 andi label the lattice sites. The algebra is realized as the Clifford algebra over a Hilbert space. The equations of motion are specified by a formal Hamiltonian of the Heisenberg form: , wheref _ij 0 and only a finite numberQ of ions are linked to any given lattice site. We prove that the Hamiltonian is non-negative in a representation of , and has a ground state exhibiting ferromagnetism. The time displacement group acts continuously on , inducing automorphisms. is asymptotically abelian with respect to the space translations of the lattice.The model is an example of an algebraic quantum field theory and possesses a broken symmetry, the rotation group 0(3). The consequent Goldstone theorem is proved, namely, there is no energy gap in the spectrum ofH.