Nonlinear optical effects for plasma diagnostics

Experimental investigations show that the 1/f noise intensityC and the contact resistanceR can be used to analyse contacts. The simply prepared contacts are fritted by discharging a capacitor, resulting in a multi-spot contact. A model relatesC andR to a number of contact spotsk with radiusa. More impulse-frittings at increasing energies decreaseC andR, thus enhancing the values ofk anda. From experimentalC vsR plots two regions are determined for GaAs: A fritting (a=constant) and A+B fritting (a∝k). Calculated values ofk are in good agreement with the number of peaks or pits formed by etching the semiconductor surface. From experimentalC vsW orR vsW curves, withW the cumulative impulse-fritting energy, the conclusion can be made thatka ³ is proportional toW.     

A new method for constructing factorisable representations for current groups and current algebras

LetC _e (R ⁿ ,G) denote the group of infinitely differentiable maps fromn-dimensional Euclidean space into a simply connected and connected Lie group, which have compact support. This paper introduces a class of factorisable unitary representations ofC _e (R ⁿ ,G) with the property that the unitary operatorU _f corresponding to a functionf inC _e (R ⁿ ,G) depends not only onf, but also on the derivatives off up to a certain order. In particular these representations can not be extended to the group of all continuous functions fromR ⁿ toG with compact support.     

The neutron/proton ratio of fast nucleon emission in antiproton annihilation on nuclei

The measurement of fast protons and neutrons emitted after antiproton annihilation at rest on²³⁸U and⁶³Cu reveals a large neutron/proton ratioR. Its value for⁶³Cu is larger than expected from the conventional model of intranuclear pion rescattering. A value ofR essentially constant over the whole range of mass number, from¹²C up to²³⁸U, is also announced by the experimentalists. It is shown that, on the contrary, the conventional scheme predicts a regular increase ofR with mass number. Alternative explanations of the effect are looked for. Within the usual scheme, an excess of negative pions, leading to more emitted neutrons, is not compatible with final pion multiplicities. The influence of meson resonances on the neutron/proton ratio is considered, as well as the possible occurrence of annihilations on two nucleons. They cannot warrant an increase ofR at low mass targets sufficient to explain a constant value over the whole range of target masses.     

Chaotic properties of multipoint correlation functions of an Ising model with long-range interactions on the Sierpiński—Gasket lattice

A class of multispin correlation functions of an Ising model with ferromagnetic nearest neighbor interactionsK and constant (distance-independent) long-range interactionsQ ₁=Q,l=1,2,..., on the Sierpiski-gasket lattice is considered. Using an exact method for calculating thermodynamic functions of hierarchically constructed Ising systems, it is shown that, for a set of values ofQ and for almost all values ofK, someM _k-spin correlation functions, whereM _k=3 ^k +3 withk=1,2,...,n andn=1,2,... being the order of lattice construction, change chaotically asn, k, and therebyM _k increase to infinity. Accordingly, in the thermodynamic limit, these correlation functions prove to be nonanalytic for appropriate values ofQ andK. SinceM _k-point correlation functions withk being finite, i.e., correlation functions involving finite numbers of spins, remain analytic asn tends to infinity, there is a smooth crossover between analytic properties of correlation functions of the two types.     

Magnetic field alignment of high-T c superconductorsRBa2Cu3O7–δ (R=rare earth)

Finely ground powders ofRBa₂Cu₃O_{7 –} (R=Y, Nd, Sm, Eu, Dy, Ho, Er, Tm, Yb) have been mixed at dilute 3%-by-volume concentrations into epoxy matrices which were then allowed to harden in applied magnetic fieldsH _A=18 kOe. X-ray diffractometry studies and 4.3 K measurements of supercurrent-induced magnetization hysteresisM are interpreted as indicating at least partial alignment of single-crystal-grain c-axes (1) parallel toH _A forR=Y, Nd, Sm, Dy, Ho (as earlier found by Farrell et al. forR=Y), and (2) perpendicular toH _A forR=Eu, Er, Tm, Yb. With a few exceptions (Y, Sm, Eu) the alignment direction correlates with the sign of the second-order Stevens factor _J of the crystalline electric field Hamiltonian in the manner suggested by Livingston et al. For the best aligned specimens (Ho, Dy) critical current densitiesJ _c (4.3 K, 5 kOe) for individual grains are estimated fromM and the Bean model to be of order 10⁷ A/cm² for the measuring fieldH parallel to the original alignment fieldH _A, and of order 10⁶ A/cm² forH perpendicular toH _A.     

On the determination of elliptic differential and finite difference operators in vector bundles overS 1

For an elliptic differential operatorA overS ¹, , withA _k (x) in END(^r) and as a principal angle, the -regularized determinant Det A is computed in terms of the monodromy mapP _A , associated toA and some invariant expressed in terms ofA _n andA _n–1 . A similar formula holds for finite difference operators. A number of applications and implications are given. In particular we present a formula for the signature ofA whenA is self adjoint and show that the determinant ofA is the limit of a sequence of computable expressions involving determinants of difference approximation ofA.Partially supported by an NSF grant     

Continuity of percolation probability on hyperbolic graphs

LetT _k be a forwarding tree of degreek where each vertex other than the origin hask children and one parent and the origin hask children but no parent (k2). DefineG to be the graph obtained by adding toT _k nearest neighbor bonds connecting the vertices which are in the same generation.G is regarded as a discretization of the hyperbolic planeH ² in the same sense thatZ ^d is a discretization ofR ^d . Independent percolation onG has been proved to have multiple phase transitions. We prove that the percolation probabilityO(p) is continuous on [0,1] as a function ofp.     

Almost periodic Schrödinger operators

We discuss the absolutely continuous spectrum ofH=?d ²/dx ²+V(x) withV almost periodic and its discrete analog (hu)(n)=u(n+1)+u(n?1)+V(n)u(n). Especial attention is paid to the set,A, of energies where the Lyaponov exponent vanishes. This set is known to be the essential support of the a.c. part of the spectral measure. We prove for a.e.V in the hull and a.e.E inA, H andh have continuum eigenfunctions,u, with |u| almost periodic. In the discrete case, we prove that |A|≦4 with equality only ifV=const. Ifk is the integrated density of states, we prove thaton A, 2kdk/dE≧π^?2 in the continuum case and that 2π sinπkdk/dE≧1 in the discrete case. We also provide a new proof of the Pastur-Ishii theorem and that the multiplicity of the absolutely continuous spectrum is 2.     

W-geometry of the Toda systems associated with non-exceptional simple Lie algebras

The present paper describes theW-geometry of the Abelian finite non-periodic (conformal) Toda systems associated with theB, C andD series of the simple Lie algebras endowed with the canonical gradation. The principal tool here is a generalization of the classical Plücker embedding of theA-case to the flag manifolds associated with the fundamental representations ofB _n ,C _n andD _n , and a direct proof that the corresponding Kähler potentials satisfy the system of two-dimensional finite non-periodic (conformal) Toda equations. It is shown that theW-geometry of the type mentioned above coincide with the differential geometry of special holomorphic (W) surfaces in target spaces which are submanifolds (quadrics) ofCP ^N with appropriate choices ofN. In addition, theseW-surfaces are defined to satisfy quadratic holomorphic differential conditions that ensure consistency of the generalized Plücker embedding. These conditions are automatically fulfilled when Toda equations hold.Unité Propre du Centre National de la Recherche Scientifique, associée à l'École Normale Supérieure et à l'Université de Paris-Sud.     

Anisotropic impurity scattering in palladium silver alloys

Measurements have been made of the Hall coefficientR of some alloys of silver in palladium over the temperature range 1°K to 120°K. The alloys contain between ∼1 and ∼10 at.-% silver. Values ofR were also obtained at room temperature and these were in good agreement with earlier published work. The values ofR are negative in all the alloys, and |R| increases both on reducing the temperature and increasing the silver concentration,c. Below ∼10°K, |R| becomes independent of temperature but shows a linear dependence onc, increasing by a factor of 2.5 over the concentration range measured. This increase is too great to be accounted for in terms of band structure changes alone, so we have examined the effects of anisotropic impurity scattering. To a first approximation it can be shown thatR is proportional to an anisotropy parameterA, defined asA=〈τ ²(k)〉/〈τ(k)〉², whereτ(k) represents the relaxation time of an electron in a statek, and 〈〉 is an average over the Fermi surface. In palladium we assume that the majority of the current is carried by the s-electrons. In the presence of silver impurities these electrons can be scattered into s-states or d-states with relaxation times given byτ _ss α1/c(1−c) andτ _sd α1/c ²(1−c) respectively. FollowingPlate we have assumed thatτ _ss is isotropic and thatτ _sd is anisotropic, leading to an overall anisotropic relaxation time for impurity scattering. We then find the parameterA increases approximately linearly with silver content, in accordance with our experimental results.