The spectrum of a quasiperiodic Schrödinger operator

The spectrum (H) of the tight binding Fibonacci Hamiltonian (H _mn= _m,n+1+ _m+1,n + _m,n v(n),v(n)= ((n–1)), 1/ is the golden number) is shown to coincide with the dynamical spectrum, the set on which an infinite subsequence of traces of transfer matrices is bounded. The point spectrum is absent for any , and (H) is a Cantor set for 4. Combining this with Casdagli's earlier result, one finds that the spectrum is singular continuous for 16.On leave from the Central Research Institute for Physics, Budapest, Hungary     

Bound on the Q-Factor of a G-Constant Measuring Pendulum Device from Gravitational Stochastic Background

We discuss the possible effects of gravitational-wave stochastic background on the performance of a pendulum device such those used in precise measurements of the gravitational constant G. The variation Q of the quality factor Q of the pendulum induced by the stochastic background is evaluated, by using as numerical input the results obtained in gravitational antennas experiments. It is found |q|10^–10, completely negligible with respect to a typical value Q10⁵.     

Standpoint cosmology

An unorthodox cosmology is based on a notion of standpoint, distinguishing past from future, realized through Hilbert-space representation of the complex conformai group for 3+1spacetime and associated coherent states. Physical (approximate) symmetry attaches to eight-parameter complex Poincaré displacements, interpretable as growth of standpoint age (one parameter), boost of matter energy-momentum in standpoint rest frame (three parameters) and displacement of matter location in a compact U(1)O(4)/O(3) spacetime attached to standpoint (four parameters). An initial condition (at big bang) is characterized by a huge dimensionless parameter that breaks dilation invariance. Four major length scales are recognized, called Planck, particle, lab, and Hubble, with separations controlled by ; all physical concepts, including spacetime, depend on wideness of scale separation.     

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.     

Asymptotics of decay of correlations for lattice spin fields at high temperatures. I. The Ising model

We find the asymptotic decrease of correlations < _{A +y} , _B >,yZ ^v +1, |y|, in the Ising model at high temperatures. For the case when monomials _A and _B both are odd, using the saddle-point method, we find the asymptotics of the correlations for any dimension . For even monomials _A , _B we formulate a general hypothesis about the form of the asymptotics and confirm it in two cases: (1) =1 and the vectory has an arbitrary direction, (2)y is directed along a fixed axis and arbitrary . Here we use besides the saddle-point method, some arguments from scattering theory.     

Search for right-handed currents in muon decay

We report new limits on right-handed currents, based on precise measurements of the endpoint of the e⁺ spectrum from ⁺ decay. Highly polarized ⁺ from the TRIUMF surface beam were stopped in pure metal foils within either an 1.1-T spin-holding logitudinal field, or a 70-gauss spin-precessing transverse field. Decay e⁺ emitted within 200 mrad of the beam direction were momentum-analyzed to ±0.2%. For the spin-held data, decay via (V-A) currents requires the e⁺ rate to approach zero in the beam direction at the endpoint. Measurement of this rate sets the 90%-confidence limits P />0.9959 and M(W_R)>380 GeV, where W_R is the possible right-handed gauge boson. For the spin-precessed data we independently determine a 90% confidence limit P />0.9918.We are indebted to the entire TRIUMF management and staff for their splendid support of this experiment. In its early stages we benefited from discussion with J. Brewer, R. Cahn, K. Crowe, and W. Wenzel. Rapid commissioning of the polarimeter was made possible by the superb efforts of the LBL support staff. This research was supported in part by the U.S. Department of Energy, Division of Basic Energy Sciences, Office of Energy Research under contracts W-7405-ENG-48 and AC02-ER02289.     

Effect of Nd on the Superconductivity of Nd1+x Ba2-x Cu3O y with 0.1 ≤ x ≤ 0.35

The effect of Nd substitution at the Ba sites has been studied in Nd_1+x Ba_2-x Cu₃O _y system for 0.1 x 0.35. Orthorhombic to tetragonal structural phase transition occurs at about x = 0.17. With the increase of Nd, the T _c value decreases and T increases, where T is the difference between the onset and critical temperatures and indicates the sharpness of the transition. These changes are explained by ac-susceptibility measurements on Nd_1.1Ba_1.9Cu₃O_7.12 at 0.10 Oe. The susceptibility curves show the presence of about four phases, which are not detectable by X-ray diffraction technique.     

Ferromagnetic resonance in thin cobalt films

The paper gives the results of measuring ferromagnetic resonance on thin cobalt films, vacuum deposited on unheated glass slides. The values of the (g-factor, the width of the curve, the effective stress and uniaxial induced anisotropy were determined as a function of the thickness of the film from measurements of the ferromagnetic absorption in a magnetic field normal and parallel to the surface of the film. Measurements were carried out on a frequency of 9200 MHz and on film thicknesses of 180 to 1800 Å. A qualitative explanation of the observed dependences is given.

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, . , , g-, , , . 9200 MHz 180–1800 Å. .

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The author thanks V. Kamberský and Z. Málek, C. Sc., for providing some of the cobalt films and for help in depositing and measuring the thicknesses, S. Kadeková and M. Polcarová for valuable advice in determining the structure of the films, J. Míová for carefully plotting the results of measurements and Z. Málek and O. tirand for carefully reading the paper and for valuable discussions.     

Zeta functions and transfer operators for piecewise monotone transformations

Given a piecewise monotone transformationT of the interval and a piecewise continuous complex weight functiong of bounded variation, we prove that the Ruelle zeta function (z) of (T, g) extends meromorphically to {z<^-1} (where =lim g^°T^n-1...g^°Tg ^1/n ) and thatz is a pole of if and only ifz ^–1 is an eigenvalue of the corresponding transfer operator L. We do not assume that L leaves a reference measure invariant.Research partially supported by the Fonds National Suisse     

On scaling properties of cluster distributions in Ising models

Scaling relations of cluster distributions for the Wolff algorithm are derived. We found them to be well satisfied for the Ising model ind=3 dimensions. Using scaling and a parametrization of the cluster distribution, we determine the critical exponent/=0.516(6) with moderate effort in computing time.     

Monte Carlo study of the ising model phase transition in terms of the percolation transition of “physical clusters”

Finite squareL×L Ising lattices with ferromagnetic nearest neighbor interaction are simulated using the Swendsen-Wang cluster algorithm. Both thermal properties (internal energyU, specific heatC, magnetization |M|, susceptibility) and percolation cluster properties relating to the physical clusters, namely the Fortuin-Kasteleyn clusters (percolation probability P , percolation susceptibility _p, cluster size distributionn _l) are evaluated, paying particular attention to finite-size effects. It is shown that thermal properties can be expressed entirely in terms of cluster properties, P being identical to |M| in the thermodynamic limit, while finite-size corrections differ. In contrast, _p differs from even in the thermodynamic limit, since a fluctuation in the size of the percolating net contributes to, but not to _p. NearT _c the cluster size distribution has the scaling properties as hypothesized by earlier phenomenological theories. We also present a generalization of the Swendsen-Wang algorithm allowing one to cross over continuously to the Glauber dynamics.     

Zeros of the finite-size scaling region partition function for a model with a wetting transition

We derive a finite-size scaling representation for the partition function for an Onsager-Temperley string model with a wetting transition, and analyze the zeros of this partition function in the complex scaled coupling parameter of relevance. The system models the one-dimensional interface between two phases in a rectangular two-dimensional region (x, y) ²,–L yL,oxN. The two phases are at coexistence. The string or interface has a surface tension 2KkT per unit length and an extra Boltzmann weighta per unit length if it touches the surfaces aty=±L. There is a critical valuea _c=1/2K and fora>a _c the string is confined to one of the surfaces, while fora a _c the string moves roughly in the rectangular region. The finite-size scaling parameters are =a _c ² N/L ² and =L(a–a _c)/a _c ² . We find that for || large, the zeros of the scaled partition function lie close to the lines arg()=±/4 with re()>0. We discuss the motion of all the zeros as changes by both analytic and numerical arguments.     

Direction-direction correlations of oriented polymers

We calculate the direction-direction correlations between the tangent vectors of an oriented self-avoiding walk (SAW). LetJ (x) andJ ^v (0) be components of unit-length tangent vectors of an oriented SAW, at the spatial pointsx and 0, respectively. Then for distances |x| much less than the average distance between the endpoints of the walk, the correlation function ofJ (x) withJ ^v (0) has, ind dimensions, the form . The dimensionless amplitudek(d) is universal, and can be calculated exactly in two dimensions by using Coulomb gas techniques, where it is found to bek(2)=12/25 ². In three dimensions, the -expansion to second order in together with the exact value ofk(2)in two dimensions allows the estimatek(3)=0.0178±0.0005. In dimensionsd4, the universal amplitudek(d) of the direction-direction correlation functions of an oriented SAW is the same as the universal amplitude of the direction-direction correlation functions of an oriented random walk, and is given byk(d)= ²(d/2)/(d–2) ^d .     

Rigorous Spectral Analysis of the Metal–Insulator Transition in a Limit-Periodic Potential

We consider the limit-periodic Jacobi matrices associated with the real Julia sets of f (z)=z ²– for which [2, ) can be seen as the strength of the limit-periodic coefficients. The typical local spectral exponent of their spectral measures is shown to be a harmonic function in decreasing logarithmically from 1 to 0.     

Measurement of the refractive index and optical absorption spectra of epitaxial bismuth substituted yttrium iron garnet films at uv to near-ir wavelengths

Refractive-index and optical-absorption spectra of Bi-substituted yttrium iron garnet films, epitaxially grown by liquid-phase epitaxy, have been measured in the spectral regime 0.26 m1.9 m by thin-film interference for 0.52 m and by ellipsometry for0.52 m. The Y_3–x–y Bi _x Pb _y Fe_5–z Pt _z O₁₂ films contain bismuth in the range Ox 1.42, lead in the range 0.01 y0.08 and platinum in the range 0.005<=z0.03. There is satisfactory coincidence between the results from ellipsometry and thin-film interference in the overlapping wavelength region. The materials investigated are the same as reported earlier from this laboratory in ter mof their magnetic and magnetooptic properties.     

Current distributions in a two-dimensional random-resistor network

The current and logarithm-of-the-current distributionsn(i) andn(ln i) on bond diluted two-dimensional random-resistor networks at the percolation threshold are studied by a modified transfer matrix method. Thek th moment (–9k8) of n(ln i) i.e., ln i&^k, is found to scale with the linear sizeL as (InL)^(k). The exponents (k) are not inconsistent with the recent theoretical prediction (k)=k, with deviations which may be attributed to severe finitesize effects. For small currents, ln n(y)–, yielding information on the threshold below which the multifractality of (i) breaks down. Our numerical results for the moments of the currents are consistent with other available results.     

Continuity of type-I intermittency from a measure-theoretical point of view

We study a simple dynamical system which displays a so-called type-I intermittency bifurcation. We determine the Bowen-Ruelle measure and prove that the expectation (g) of any continuous functiong and the Kolmogoroff-Sinai entropyh() are continuous functions of the bifurcation parameter. Therefore the transition is continuous from a measure-theoretical point of view. Those results could be generalized to any similar dynamical system.     

On classical models of Spin

We discuss two classical situations that lead to probabilities characteristic for systems with spin-1/2. (a) Pitowsky model: It is demonstrated that the definition of spin functions does not imply which circle (a parallel or a great circle) on the sphere should be taken as a probability space in calculation of conditional probabilities. Pitowsky's choice of parallels must be formulated as an assumption about the model. It is shown that the model explicitly avoiding this difficulty is possible and no contradiction with the Bell Theorem is found. The modification is based on a new pathological decomposition of the sphere and belongs to a class of hidden variable theories with undetected signals. (b) Aerts model: We show the importance of the polarization effect of the measurements for the sake of obtaining a non-Kolmogorovian probability model. It is also shown that the conditioning by a change of state leads in general to the non-Kolmogorovian probability calculus.2. For example, let _{Cw,z xCw,z}µ_c ({y C _w,z S ₊|(x,y) /2})=µ _c(C _w,z S ₊)= 1/2µ _c(C _w,z). Pitowsky spheres with white points distributed onC _w,z in this way exist. The proof is exactly analogous to this of Theorem 1 in [1]. Then (**) = 1 -/, if one takesC _w,z as the probability space. This example seems very instructive.3. If the chargeq falls down on some point then it clearly has not fallen down on another one. Having given a result of a measurement we cannot, within the model with polarization, talk in a sensible way about its alternative: We can think either aboutsuccessive measurements (then the Bell inequality is not derivable) or ask What would have happened if..., but then we deal with a different problem (in Aerts' terminology [2b] this is anobservation) and obtain again Eq. (8) (there is no complementarity but there is no model of spin either).     

Light absorption by free semiconductor carriers in the presence of a laser wave

Within the framework of the conditions ; » ^–1 ( ^–1 is the mean time of momentum relaxation), the coefficient of absorption () of a weak electromagnetic wave by the free carriers of a polar semiconductor is calculated in the presence of a strong wave (of frequency ), for arbitrary values of and . Photon absorption by band electrons is due to these latter interacting with optical phonons (of frequency _o). The problem is solved by using an analogous approach to the theory of the linear Kubo reaction. The results are valid in the absence of electron heating, when a strong wave only influences the scattering probability. The appearance of a photostimulated tail of absorption is predicted for < _o, including the jump () for ( – _o + ) ₀T as well as peaks in the function () at the points _s=s (s=1, 2, 3,...). The value (₁) is determined by the formula for the absorption coefficient for one strong wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 105–109, July, 1981.The authors are grateful to É. M. Épshtein and Sh. M. Kogan for useful discussions.     

Scaling of Mandelbrot sets generated by critical point preperiodicity

Letzf (z) be a complex holomorphic function depending holomorphically on the complex parameter . If, for =0, a critical point off ₀ falls after a finite number of steps onto an unstable fixed point off ₀, then, in the parameter space, near 0, an infinity of more and more accurate copies of the Mandelbrot set appears. We compute their scaling properties.On leave from the University of Geneva