Gd3+-ESR in the intermediate valent cerium compounds Ce x La1-x Os2

In the intermediate valent compounds Ce _x La_1–x Os₂ the Gd³⁺-ESR shows a non-linear increase of the linewidth H(T) in the temperature range 4.2K<T<300K for 0.3x1.0. This non-linearity of the thermal broadening is strongly altered by changing the Ce-concentration. The experimental results H(T,x) can quantitatively be described via hybridization of conduction electrons with Ce4f electrons: Due to hybridization, the Ce4f states are broadened but remain localized. The conduction electron density of states is reduced in the vicinity of the 4f states. In addition we observe a maximum in the electrical resistivity (T) of CeOs₂ at 270 K.     

The contribution of domain walls to the small-signal complex permittivity of BaTiO3

A method is proposed for determining the contribution _w of 180° domain walls to the initial permittivity of ferroelectrics. It consists in measuring the dependence of on the mean polarization of the sampleP _a at a frequencyf>f _r , wheref _r in the case of BaTiO₃ denotes the basic resonance frequency of thickness vibrations. It is shown that the measurements of Meitzler and Stadler [7] and our measurements prove the existence of _w in the regionf _r 3 crystal _w =15 to 30, _w =1 to 5. The existence of _w for low frequencies (f _r ), where the clamping effect occurs [6], is discussed.The author is indebted to O. Sedmík and V. Janouek for help in the measurements. He also thanks Dr. A. Fousková and Dr. V. Janovec for stimulating discussions and Dr. V. Dvoák and Dr. J. Kaczér for valuable remarks on the paper.     

Quantitative determination of defocus,thickness and composition from high-resolution transmission electron microscopy lattice images

A quantitative method for the direct determination of defocusf, local thickness t and local compositionx from high-resolution transmission electron microscopy lattice images of wedge-shaped crystal samples is proposed. The method relies on the analytically derived relation between the first-order linear and nonlinear image Fourier coefficientsJ ₁ andJ ₂ onf,t andx. By plotting J1 VSJ ₂ for varying t, ellipses with defocus- and composition-specific geometry are obtained. By reconstructing the appropriate ellipse for image regions of homogeneous composition, f and t can be determined independently. At interfaces, local compositionsx can be determined within the full range 0 x 1 by utilizing systematic variations of the ellipse's geometry with varyingx.     

Density of states for intermediate valence and Kondo systems

We calculate the density of states for the nondegenerate Anderson model for various values ofu=U/ andn _f using the perturbation theory withu as the expansion parameter. Summing all the -independent self-energy diagrams, we use the Friedel sum rule and Ward identities to express the physical quantities in terms of the remaining -dependent part of the self-energy, which we evaluate to the 2nd order. The results for the spin and charge susceptibilities obtained in such a way compare rather well with the Bethe-ansatz results. The density of states exhibits different features in different parts of the parameter space. In Kondo region (u>1,n _f 1, i.e., – _f ~U/2), we obtain a many-body resonance (half-width T _K ) around the Fermi level and two broad peaks () at about _f +n _f U and _f +U. In the VF region (u>1, and | _f |) we obtain only two peaks (), one at about _f and one between _f +n _f U and _f +U. The consequences regarding the shape of the photoemission and inverse photoemission spectra of Ce intermetallics are discussed.     

Contribution of quantum corrections and superconducting fluctuations to the magnetic field and temperature dependence of the conductivity in amorphous CuTi and CuZr alloys

We report conductivity measurements on Cu _x Ti_100–x and Cu _x Zr_100–x glasses as a function of magnetic field (0B6T) and temperature (1.5–5. At low temperatures the measured conductivity(T,B)= ₀+(T)+(B,T) is compared quantitatively with the predictions of diagrammatic perturbation theories including quantum interference effects, spin-orbit scattering and electron-electron interaction. We obtain a set of characteristic fields for inelastic and spin orbit scattering from both the magnetic field and the temperature dependence of the measured (T, B). Below about 4K the Coulomb interaction determines (T) in consistence with the Hall effect, whereas quantum interference processes and spin-orbit scattering dominate the magnetic field dependence. In case of Cu _x Zr_100–x , (B, T) can be explained by taking into account superconducting fluctuations (Maki-Thompson and Aslamasov-Larkin parts) in addition. Superconducting fluctuations dominate the temperature dependence as well. For high magnetic fields and lower temperatures (B/T>1T/K) we find discrepancies between experiment and calculations from perturbation theory.     

Debye screening for two-dimensional Coulomb systems at high temperatures

The grand canonical ensemble of a two-dimensional Coulomb system with±1 charges is proved to have screening phenomena in its high-temperature region. The Coulomb potential in a finite region is assumed to be (–)^–1, where is the Laplacian with zero boundary conditions on. The hard-core condition is not assumed. The model is set up by separating (–)^–1 into a shortrange part and a long-range part depending on a parameter. The self-energies are subtracted only for the short-range part and therefore a choice of is a choice of subtraction of self-energies. The method of proof is in general the same as that of Brydges-Federbush Debye screening, except that here a modification for the short-range part of the potentials is needed.     

Expectation values of unbounded observables

For an unbounded quantum mechanical observableA, the expectation value A _f and the mean square deviation _f A cannot be denned for all (pure) statesf by A _f = (f,Af) and ( _f A)² = (f,A ² f)-(f,Af)², respectively. More general definitions are given here, which are also valid for state mixtures (density matrices). A general uncertainty relation for unbounded observables is derived.     

On the failure of the time-energy uncertainty principle

We establish, for the quantum system made up of a single free particle, the formula E t(v/c) , where E is the precision to whichE can be ascertained in time t. The measurement can be carried out with zero disturbance inE itself.     

Exponential decay in the stark effect

LetH=–+V+Fx ₁ withV(x ₁,x ) analytic in the first variable andV(x ₁+ia, x ) bounded and decreasing to zero asx for eacha . Let be an eigenvector of –+V with negative eigenvalue. Among our results we show that forF0, (,e ^–H ) decays exponentially at a rate governed by the positions of the resonances ofH. This exponential decay is in marked contrast to conventional atomic resonances for which power law decay is the rule.Research supported by NSF Grant No. MCS 78-00101.     

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–).     

Spatio-temporal Fourier components and soft modes in thermal convection: A neutron scattering study

In a nematic liquid crystal subjected to a vertical temperature difference T in a vertical slab container, we find, using real-time and real-space neutron scattering, that the spatiotemporal pattern can be indexed on a two-dimensional lattice with selection rule (h+k)=2n. Higher index modes are sequentially activated as T increases from the convection threshold T _c . The frequency softening as TT _c and asTT ₀, the super-cooling limit of the nematic, is discussed.     

Mass-Proper Time Uncertainty Relation in a Manifestly Covariant Relativistic Statistical Mechanics

We prove the uncertainty relation T _V m2/c ², which is realized on a statistical mechanical level for an ensemble of events in (1+D)-dimensional spacetime with motion parameterized by an invariant proper time , where T _V is the average passage interval in for the events which pass through a small (typical) (1+D)-volume V, and m is the dispersion of mass around its on-shell value in such an ensemble. We show that a linear mass spectrum is a completely general property of a (1+D)-dimensional off-shell theory.On sabbatical leave from School of Physics and Astronomy, Tel Aviv Uniersity, Ramat Aviv, Israel. Also at Department of Physics, Bar-Ilan University, Ramat-Gan, Israel     

Extending Heisenberg's Measurement-Disturbance Relation to the Twin-Slit Case

Heisenberg's position-measurement-momentum-disturbance relation is derivable from the uncertainty relation (q)(p) h/2 only for the case when the particle is initially in a momentum eigenstate. Here I derive a new measurement-disturbance relation which applies when the particle is prepared in a twin-slit superposition and the measurement can determine at which slit the particle is present. The relation is d × p 2h/, where d is the slit separation and p = D_M(P_f, P_i) is the Monge distance between the initial P_i(p) and final P_f(p) momentum distributions.     

Self-consistent calculation of statics and dynamics of the roughening transition

Statics and dynamics of the modified kinetic discrete Gaussian model are treated selfconsistently using a Gaussian probability assumption. A non-trivial roughening temperatureT _R is found in exactly two dimensions only. The free energyF, the correlation length and the interface roughness h ² are found to behave—lnFlnh ²(T _R –T)^–1 for temperaturesT approachingT _R from below. The linear relaxation rate of the order parameter is found to be proportional to ^–2. As a model for crystal growth, the growth rate depends linearly upon the chemical potential difference aboveT _R , shows a metastable regime belowT _R with a spinodal limit of metastability _c , beyond which oscillatory growth starts. The critical behavior of _c is found to be ln _c –(T _R –T)^–1+O(ln (T _R –T)).     

Long-range order in the XXZ model

The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficiently low temperatures for any anisotropy(0) ifS1, and for 0<0.29 (XY-like) or>1.19 (Ising-like) ifS=1/2. In two dimensions (the square lattice), ground-state long-range order exists under the following conditions: for any anisotropy (0) ifS3/2; 0<0.032 (XY-like) or 0.67<<1.34 (almost isotropic) or>1.80 (Ising-like) ifS=1;>1.93 (Ising-like) ifS=1/2. We conjecture that the two-dimensional spin-1/2XY model (=0) has finite ground-state long-range order. Numerical evidence supporting this conjecture is given.     

InGaAs/GaAs multiple-quantum-well modulators and switches

The design, fabrication and characterization of electrooptical modulators and switches based on pseudomorphic InGaAs/GaAs multiple-quantum-well (MQW) structures is presented. The absorption and refractive index changes (, n) of In_0.2Ga_0.8As/GaAs MQW structures due to the quantum-confined Stark effect are examined in detail. The figures of merit /₀ and n/₀ give information on the design of modulation and switching devices. Based on these results, we develop two types of efficient and high-speed modulators, vertical and waveguide modulators, and for the first time an InGaAs/GaAs intersectional X-type switch. Recent experimental results for each device are presented.     

Anisotropy of the low temperature resistivity of hexagonal single crystalline spin glass systems

The impurity contribution to the resistivity in zero field (T) of dilute hexagonal single crystals of ZnMn, CdMn and MgMn has been studied in the mK range on samples cut parallel () and perpendicular () to thec-axis, using a SQUID technique for the measurements. Typical spin glass behavior is found in (T) as well as (T) for all alloys, with Kondo like logarithmic increases at higher temperatures and maxima atT _m at lower temperatures, indicating the influence of impurity interactions. The differences in the corresponding isotropic resistivity _poly(T) between the three systems can qualitatively be understood within the framework of a theoretical model by Larsen, describing (T) as a function of universal quantitiesT/T _K and _RKKY/T _K , where _RKKY is the RKKY-interaction strength andT _K the Kondo temperature. With respect to the two lattice directions studied, the behavior of (T and (T is anisotropic in the Kondo regime as well as in the range where ordering becomes important. While the anisotropy in the Kondo slope can be understood by an anisotropic unitarity limit, the understanding of the anisotropy in region where impurity interactions are important remains problematic.Dedicated to Prof. Dr. S. Methfessel on the occasion of his 60th birthday     

Relationship between field shift and phase constant change in two-dimensional three-layered dielectric or hollow waveguides due to uniform bends

It is shown theoretically that the field shift x and phase constant change in two-dimensional three-layered dielectric or hollow waveguides bent uniformly with large bending radiusR are related by x = 2R/ ₀, where ₀ is the axial phase constant. The relationship predicts that the field distributions of the TE₀ or TM₀ mode shift toward the outward direction of bending, whereas those of other TE _n or TM _n (n=1,2,...) modes shift inward in a hollow waveguide. Characteristic features in dielectric waveguides are also described.     

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)     

Mates toE=mc 2 and to the Heisenberg uncertainty relations

E=mc ² is found to be a special case ofE= ^±1cⁿ, where is any one of four susceptibilities, namely electric, magnetic, gravitational, and elastic. Letl be length,t time,t time dilation, andl a measure of Fitzgerald-Lorentz contraction. A particle is stated to be the manifestation of a collection of susceptibilities which arise when(l)/1=(t)/t. Then(E)/E=5 (t)/2t=±()/. Corresponding to susceptibility, special energy particles are postulated which exhibitSU(3) symmetry, Related to the susceptibilities are five new Heisenberg uncertainty relations. Three new conservation laws for particles are proposed.