Planar microwave biased RF-SQUIDs in niobium technology

A planar version of microwave biased SQUIDs is described. In this type of SQUID, a superconducting half-wavelength microstrip resonator serves as tank circuit, into which the SQUID is integrated. For evaluation of this type of SQUID, samples were prepared from thin Nb films on sapphire substrates, using tunnel junctions as Josephson elements. When operated in hysteretic mode, signal voltages of up to 80 V were achieved, corresponding to a flux noise of 4×10^–6 ₀/Hz and an energy resolution of 2×10^–31 J/Hz.     

The Action of √−Δ on Weighted Sobolev Spaces

The action of – on distributions is examined within the context of weighted Sobolev spaces. The results obtained are as follows: (1) – is a continuous map of R ⁿ ), the space of rapidly decreasing functions, to L ^{2, s} (R ⁿ for any s < n/2 +1; (2) if k R and s > –n/2 – 1, then – is a continuous map from H ^{k, s} (R ⁿ ), the weighted Sobolev space, to H ^{k–1, t} (R ⁿ for some t. The results are optimal in a sense.     

Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.     

Characterization of high purity GaAs far-infrared photoconductors

In this paper we report the results of an extensive study on the far-infrared photoconductivity of high purityn-type GaAs. The crystal, which was grown at Max-Plank-Institute for Solid State Physics using liquid-phase epitaxy, exhibited the fine structures of the excited state transitions of the residual shallow level impurities. The major peak in the spectral response belongs to the 1s-2p transition, with its responsivity about thirty five times higher than the continuum. At 3.4K detector temperature, 625 mV bias, and 100 Hz chopping frequency the detector responsivity at 35.4 cm^–1 (279 µm) was measured to be 0.017 A/W. Under these same conditions, the NEP was 5.9×10^–14 W/Hz. The (DC) dark current at 25 mV bias was 5.6×10^–14 A.     

On the Eigenstates of the Elliptic Calogero–Moser Model

It is known that the trigonometric Calogero–Sutherland model is obtained by the trigonometric limit (–1) of the elliptic Calogero–Moser model, where (1, ) is a basic period of the elliptic function. We show that for all square-integrable eigenstates and eigenvalues of the Hamiltonian of the Calogero–Sutherland model, if exp(2–1) is small enough then there exist square-integrable eigenstates and eigenvalues of the Hamiltonian of the elliptic Calogero–Moser model which converge to the ones of the Calogero–Sutherland model for the 2-particle and the coupling constant l is positive integer cases and the 3-particle and l=1 case. In other words, we justify the regular perturbation with respect to the parameter exp(2–1). With some assumptions, we show analogous results for N-particle and l is positive integer cases.     

Sampling of free-space magnetic pulses

We report free-space detection of magnetic pulses via the Faraday effect with shot-noise limited detection. This allows a 10^–8 T / Hz magnetic field resolution. The orthogonal propagation of the optical probe beam and the THz waves demonstrate a 1.3 ps risetime with a 400 GHz frequency bandwidth. The temporal and frequency responses of several crystals are reported with a theoretical response function analysis presented. The dispersion of the magnetic pulse into the sensor crystal is illustrated with a theoretical simulation for comparison. We also contrast the properties of electro-optic sampling with this magneto-optic sampling technique.     

Electro-optic measurement of poled polymer-based asymmetric Fabry–Perot cavity

An easy way to determine linear electro-optic effect of poled polymer materials was demonstrated by polymer-based asymmetric Fabry–Perot multiple reflection cavity. The standing-free technique of the cavity and reflective light path configuration was adopted in the measurement. This method can convert probe beam from phase modulation to intensity modulation without the reference beam for electro-optic application of poled polymer. The polymer used was a disperse red 1 doped guest/host material. The principle of the system was analyzed by multiple reflection and index ellipsoid methods, and the voltage sensitivity about 6 mV/Hz of the system was obtained at 1 kHz input signal.     

Closed timelike smooth curves in the general theory of relativity

For a space-time which admits a closed timelike smooth curve it is estimated that 2 · 10^–24 · l ², where is the real time andl the spatial length associated with the timelike curve, and is the density of material.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 9, pp. 33–36, September, 1973.     

A Remark on the Use of Differential Forms for the Skyrme Problem

We introduce a formulation of the Skyrme problem using differential forms. By means of this formulation, we prove first that the homothetic map between the standard three-sphere of radius R, S³ _r R⁴, and S³ ₁ is the unique minimizer, modulo isometries, of the Skyrme energy in its homotopy class, for any R less than some critical value R₀ (3/2, 2]. We then establish a stability result for this Skyrme-form problem from which we can recover the result of M. Loss and N. S. Manton which states that this homothetic map is stable only up to R = 2.     

Positron annihilation in ionic media and an optical model of the positron

It is proposed that positron motion in quasiatomic positron + anion systems formed in anionic media can be described by a potential of the form V_eff(r) = Z_eff/r²-/r, where Z_eff is the effective charge of the nucleus, and n is the effective charge of the anion. It is shown that the positron wave function of the ground state of the quasiatomic positron + anion system in the field of such a potential is _X(r) = l/4·A_nx·r^X·e^–ar. Thus the validity of selecting a test variation positron wave function (r) = l/4·A·r·e^–ar is demonstrated for the potential V_eff = at r = 0 and V_eff = –/r for r > 0 (Gol'danskii-Prokop'ev optical positron model, Fiz. Tverd. Tela,8, 515 (1966)), belonging to the class of functions _X(r). Having the wave function _X(r) and Slater wave functions _ns,p(r) of the electrons, annihilation photon angular distribution (APAD) curves are calculated, together with halfwidths of the APAD curves and positron lifetimes _ns,p.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 52–56, May, 1990.     

Heterodyne interferometer with two spatial-separated polarization beams for nanometrology

An interferometer having accuracy in displacement measurement of <1 nm is necessary in nanometrology. To meet the requirement, the periodic nonlinearity mainly caused by polarization and frequency mixings should be less than deep sub-nanometer. In this paper, two spatial-separated polarization beams are used to avoid mixings and then the periodic nonlinearity. The developed interferometer demonstrates a periodic nonlinearity of about 25 pm and a 2 pm/Hz in displacement noise level.     

Searching for light Higgs scalar bosons in the next generation of electron-positron collider at LEP

Thee ⁺ e ^–-collider facilities at LEP II, with the CM energy S in the range 100–170 GeV, may be able to detect light Higgs bosons, assuming a high luminosity. The production cross sections of a light Higgs bosonH ⁰ in association with the neutral gauge bosonZ ⁰ are calculated for varying ranges of the CM energy expected to be available to LEP II and VLEEP (Novosibirsk) and for various values of the light Higgs mass. It is found that production cross sections are sizable in comparison with those for the very massive Higgs bosons in proton-anti(proton) supercolliders, Tevatron, Sp¯pS, and SSC, respectively. The implication of this feature is pointed out. Further, prospects for light Higgs production in association with the charged gauge bosonW ^– in ultraenergetic neutrino beams are examined.     

Quantum-limited FM-spectroscopy with a lead-salt diode laser

Ultrasensitive absorption spectroscopy of NO₂ was performed with a tunable lead-salt diode laser (TDL) using a single-tone high-frequency modulation (FM) technique. With a detection bandwidth of 200 kHz, an optical density of 2.7 × 10^–5 was detectable at SNR of 1. The detectable optical density could be further improved by reducing the detection bandwidth in agreement with the f relationship, reaching 2.5 × 10^–6 at a detection bandwidth of 1.56 kHz. Normalized to 1 Hz bandwidth, the demonstrated performance would then correspond to a detectable optical density of 5.9 × 10^–8. This detection limit agrees well with the calculated quantum limited performance based on the measured laser power, modulation index, noise figure of the electronic components, and other parameters of the apparatus. These measurements and calculations show that by implementation of the FM technique, the sensitivity of the present TDL absorption spectrometers (TDLAS) can be improved by at least a factor of 10 and possibly even of 100. Such a sensitivity improvement would greatly extend the applicability of TDLAS for trace gas analysis, especially in atmospheric monitoring.     

The energy level spacing for two harmonic oscillators with golden mean ratio of frequencies

Berry and Tabor discussed, among other things, a beautiful problem about the energy level spacing distribution for a system of two harmonic oscillators. They gave some interesting theoretical arguments which show that there is no level clustering for generic harmonic oscillators, and various numerical experiments were exposed and discussed. But the main question they posed about the existence of the limit distribution of the level spacing remained open. The present paper discusses this question in the case when the ratio of the frequencies is the golden mean =(5–1)/2. The approach enables one to study the generic case of the frequency ratio as well, which is done elsewhere.     

Experimental comparison of four-point methods for measuring the hall effect and the electrical conductivity

Four methods for measuring the Hall constant and the resistivity of thin semiconductor plates (the van der Pauw, Kon'kov, Lange, and Buchler-Pearson methods) have been experimentally checked and compared. The dependence of the corrections C_H and C _p on the ratio d/c has been studied over the range 2–10.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 12, No. 2, pp. 20–25, February, 1969.     

Physics opportunities with polarized e − and e + beams at TESLA

Beam polarization at e⁺-e^– linear colliders will be a powerful tool for high precision analyses. Often it is assumed that the full information from polarization effects is provided by polarization of the electron beam and no further information can be obtained by the simultaneous polarization of the positrons. In this paper we point out the advantages of polarizing both beams, and summarize the polarization-related results of the Higgs, Electroweak, QCD, SUSY and Alternative Theories working groups of the ECFA/DESY workshop for a planned linear collider operating in the energy range s = 500-800 GeV.     

Empty bin effect and multiple bin phenomenon in dynamical fluctuations at high energies

Intermittency and multifractality characterizing the presence of dynamical fluctuations are analysed in terms of self-similar processes of Cantor type involving the continuous spectrum of singularities. The fundamental properties of the intermittency slopes _q as well as of the strength _q and the densityf _q , of singularities depending on the order parameterq are established. It is also argued here that the intermittency arisen owing to those self-similar processes leads to such anomalous fractal dimensions and density of singularities which hardly satisfy the assumptions allowing the interpretation of intermittency in terms of thermal as well as non-thermal phase transitions. Four concrete cases are discussed in the present contribution: the e⁺ e^– annihilations at s=29 GeV, the ¯pp interactions at s=1800 GeV, the collisions of 200 GeV/ nucleon¹⁶0 beams with the¹²C nuclei and the¹⁹⁷Au nuclei of energy 1 GeV/ nucleon break up into fragments when interacting with the nuclear emulsion. The corresponding data published so far reveal the fundamental properties following from the aforementioned processes with great accuracy.The author expresses his thanks to M. Markytan, H. Dibon and W. Kittel for fruitful discussions and F. Rimondi for providing him with the preliminary ¯pp data.     

A Note on Static Solutions of a Lorentz Invariant Equation in Dimension 3

Cut-and-project sets with convex acceptance windows, based on irrationalities = (1+5), =1+2, =2+3 are models for experimentally observed quasicrystals – materials with diffraction patterns consisting of sharp Bragg peaks in crystallographically disallowed patterns. We show that for each of these three irrationalities there exists a unique binary operation of the type x _s y:=sx+(1–s)y, such that one-dimensional cut-and-project sets are precisely Delone sets closed under this operation.     

Investigation of β–ν Angular Correlation in the β+ Decay of 18Ne and 14O

The – angular correlation in the ⁺ decay of ¹⁸Ne and ¹⁴O has been investigated using a new experimental technique. The technique is based on the precise measurement of the energy Doppler shift of a -quantum following the ^± decay. The measurement with the ¹⁸Ne isotope gives the – angular correlation coefficient = +1.06 ±0.19 which corresponds to a constraint on the scalar interaction of {|C_S|²+|C'_S|²} 0.29|C _V|. An inter-atomic interaction between the ¹⁴O daughter atom (¹⁴N) and a CO complex has been studied in a measurement with the ¹⁴O isotope.     

On “hyperboloidal” Cauchy data for vacuum einstein equations and obstructions to smoothness of Scri

The relationship between the geometric properties of hyperboloidal Cauchy data for vacuum Einstein equations at the conformal boundary of the initial data surface and between the space-time geometry is analyzed in detail. We prove that a necessary condition for existence of a smooth or a polyhomogeneous Scri (i.e., a Scri around which the metric is expandable in terms ofr ^–j log ⁱ r rather than in terms ofr ^–j ) is the vanishing of the shear of the conformal boundary of the initial data surface. We derive the boundary constraints which have to be satisfied by an initial data set for compatibility with Friedrich's conformal framework. We show that a sufficient condition for existence of a smooth Scri (not necessarily complete) is the vanishing of the shear of the conformal boundary of the initial data surface and smoothness up to boundary of the conformally rescaled initial data. We also show that the occurrence of some log terms in an asymptotic expansion at the conformal boundary of solutions of the constraint equations is related to the non-vanishing of the Weyl tensor at the conformal boundary.Supported in part by KBN grant #2 1047 91 01