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.     

The theory of neutron scattering from mixed harmonic solids

In the intermediate valent cerium alloys Ce_1–xY_xPd₃, Ce(Pd_1–xRh_x)₃ and Ce(Pd_1–xAg_x)₃ the Gd³⁺-ESR shows a non-linear increase of the linewidth H(T) in the temperature range 4.2KT300K. The deviation from the linear Korringa law can be described by a reduced conduction electron density of states at the Gd site (which is a Ce lattice site) in the energy range E _4f (=width of the Ce 4f states). This supposition allows a determination of E _4f from the H(T)-data. For CePd₃:Gd³⁺ we find E _4f=(650±100) K. E _4f increases with Y- and Rh-concentration and decreases with Ag-concentration.     

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     

Error performance analysis for an optical heterodyne FSK communication system with a limiter-discriminator-integrator detector

The error probability for a coherent optical heterodyne FSK system with a limiter-discriminator-integrator (LDI) detector is analysed. The analysis includes laser quantum phase noise, the correlated receiver additive white Gaussian noise (AWGN), Gaussian narrow-band IF filtering and intersymbol interference (ISI) caused by it. It is shown that, for 1 dBEb/N ₀penalty at bit error rate (BER) 10^–9, (i) the normalized IF beat spectral linewidth T0.35% for frequency deviation ratioh=0.5(MSK), and T0.5% forh=0.7 (the receiver is insensitive to laser quantum phase noise ath=1.0, if ISI is not included.); (ii) if ISI is incorporated, T0.15% forh=0.5, T0.5% forh=0.7, both with 3dB bandwidth-bit period product (3.0>BT1.5), and T0.5% forh=1.0 with BT1.0 ifT0.35% when ISI exists,h=0.7 is optimum;h=1.0 otherwise.     

T c =0-Ordering in the ruby Ising-spin glass?

Isothermal and adiabatic susceptibilities characterize the rubies under investigation, (Cr _x Al_1–x )₂O₃ with 0.00025x0.008, as symmetric Ising spin glasses with a rms interaction of . Spin-freezing phenomena, like cusps, plateaus, and thermoremanence in the low-field magnetization are associated with a restricted heat transfer between the spin system and the thermal bath in the precritical region (TJ). At equilibrium andTJ, the scaling of the non-linear magnetization and the slowing down of the zerofield, average relaxation rate indicate a spin glass transition atT _c =0. Among possible reasons for this apparent discrepancy to theT _c J-hypothesis by Ogielski et al., are internal random fields.     

Soft mode dynamics and spatio-temporal symmetry breaking in a thermo-convective system

Using neutron scattering we have studied the behaviour of an oscillatory soft mode in a thermoconvective liquid crystal. As a function of an applied vertical temperature difference T the behaviour of the soft-mode frequency defines four regimes, separated by cross-over values at which spatio-temporal symmetry is broken. Breaking of time symmetry manifests itself in different phase relations among localized oscillators. Incomplete softening at the convection threshold T _c is interpreted as anharmonic coupling to low-energy, internal director fluctuations in the nematic. Subtracting the anharmonic contribution, the renormalized frequency squared gives a susceptibility critical index for each of the four regimes. The values range between 1.1 and 2.7, indicative of a change of the spatial dimensionality as TT _c. The widths in T of the regimes converge as the Feigenbaum ratio (4.6), and the meaning of this is discussed.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Spin-wave analysis of easy-axis quantum antiferromagnets on the triangular lattice

We perform the standard spin wave analysis of the triangular Heisenberg quantum antiferromagnet with nearest neighbour coupling. The exchange interaction is taken to be J _{z=J x=J y} (0<1). We give a simple explanation of the non-trivial classical degeneracy pointed out by Miyashita and Kawamura and show that it is removed by quantum fluctuations, but that the degeneracy manifests itself through the appearance of a second gapless spin-wave branch. The existence of a second gapless mode has a drastic influence on the quasiclassical behaviour near the Ising limit: the energy gain with respect to the Ising state energy is found to be linear in , and the reduction of the sublattice magnetization on two of the three sublattices remains finite as 0. These findings essentially invalidate the original qualitative arguments [14] in favour of a spin-liquid ground state of the anisotropic triangular antiferromagnet.     

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.     

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)).     

Mössbauer study of oxygen-related lattice instabilities in oriented 1-2-3 HTSC

⁵⁷Fe Mössbauer effect measurements as a function of temperature between 78 and 293 K in grain-aligned YBaCuO (T _c=89 K, T _c<2 K) with bothc andc orientations revealed a sequence of anomalies in the recoilless fraction, center shift and linewidth of all⁵⁷Fe quadrupole doublets in the host lattice. These anomalies are believed to arise due to antiferroelectric phase transitions driven by a nonlinear anharmonic vibrational motion of oxygen atoms in a breathing mode configuration. The results obtained are indicative of a possible coexistence of high-T _c superconductivity and antiferroelectricity in 1-2-3 ceramics.     

Far-infrared spectroscopy of the supreconductor YBa2Cu4O8

The frequencies of allB _1u (z) phonon modes predicted by a group-theoretical analysis were measured and found to agree well with recent lattice dynamical calculations for this compound. We report also the determination of two superconducting gap values in YBa₂Cu₄O₈ through phonon self-energy effects in the normal and superconducting conducting state. The gap-to-T _c ratios obtained from an analysis of these effects are 2 ₁/kT _c 2.5 and 5.82 ₂/kT _c 9.2. This coincides with previous results of both phononic and electronic Raman scattering where values of 2.1 and 6.3 were found. We further find anomalous softenings of two phonon modes 40 Kabove T _c , which correlate with an observed deviation from the linear temperature dependence of the average plasma frequency _p (T).     

Harmonic mixing by weakly pinned charge density waves

Third order harmonic mixing voltageE ₀ in case of frequency matching, =₂–₁=0, and third order pseudo harmonic mixing currentj() in the detuned case, 0, are evaluated for the one-dimensional Fukuyama-Lee-Rice model for weakly pinned charge density waves in the region of sub-threshold bias electric fields. After a perturbation expansion of the phase response to the ac driving fields the impurity averaging is performed diagrammatically. Specific statistical properties of the charge density wave phase in the weak pinning limit and a non-trivial result for the pinning of the static phase are utilized to expressE ₀ andj() in terms of the dielectric function (). A recent evaluation of () within the self-consistent Born approximation is used to present the results explicitly in a number of diagrams. In comparison to the overdamped anharmonic oscillator the following differences are found: Randomness leads to interference contributions which increase the amplitudes and decrease the phase shifts. The more realistic form for () at lower frequencies lead to a downward shift in the maximum ofj() when ₁ is decreased below the cross-over frequency _c . The present theory retains inertia in the dynamical equations and remains valid for frequencies near and above the pinning frequency. It fails, however, for small frequencies _{1 c} due to the neglect of metastable states and screening.     

The Yang-Lee edge singularity in spherical models

The density of Yang-Lee zeros in the thermodynamic limit is discussed for ferromagnetic spherical models of general dimensionalities and arbitrary range of interaction. In all cases the zeros lie on the imaginary axis in the complex magnetic field planeH=H+iH with a density (H) that exhibits a square root singularity(H) (H-H ₀), with=1/2, as the edge of the gap atH=H ₀(T) is approached forT>T _c. WhenTT _c one hasH ₀(T)(TT _c ) with critical exponent=+.Supported by the National Science Foundation in part through the Materials Science Center at Cornell University.     

Behavior of the electrical resistivity at phase transitions in binary alloys

The excess resistivity of binary alloys is calculated in the Born approximation for the scattering of quasifree electrons from the atomic disorder. can be represented as the convolution of the structure functionS(q) and the fourier transform of the effective potential. The critical anomaly of is derived from scaling expressions forS(q), both for alloys which undergo unmixing and for order-disorder transitions. The variation of with concentration and temperature in the vicinity of a critical point is obtained. The time-dependence of the resistivity of alloys after a sudden quench into the two-phase region is also calculated, using computer simulation data forS(q,t), and a maximum of is found for zones with linear dimension of 8–12 lattice spacings. All these results are in fair agreement with the available experiments. As a further possible application, we obtain the critical exponent for the nonlinear relaxation of the resistivity of an alloy close to the order-disorder transition.     

Exact Relations Between Elastic and Electrical Response of d-Dimensional Percolating Networks with Angle-Bending Forces

Arguments are presented to demonstrate that exact equality relations exist between the critical exponents which characterize the macroscopic conductivity _e and the macroscopic elastic stiffness moduli C _e of percolating systems of any dimensionality. Using the notation _e p ^t , C _e p ^T for the critical behavior of a randomly diluted system slightly above the percolation threshold p _c , (pp–p _c >0) and _e |p|^–s , C _e |p|^–S for the critical behavior of a random mixture of normal and perfectly conducting or normal and perfectly rigid constituents slightly below that threshold, (pp–p _c <0) we show that T=t+2 and S=s, where is the percolation correlation length critical exponent |p|^– (p0).     

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     

Representations of state space transformations by Markov kernels

Every convex subset of a locally convex Hausdorff space (X, ) is equipped with the (-algebra generated by its-relatively open subsets. Within the set () of probability measures on two particular convex subsets are considered: (a) the set ^s () of probability measures with a separable support, and (b) the set ^c () of probability measures with a compact convex support. If is the base of a cone inX, then there exists an affine barycenter map from ^c () onto whose composition with the natural embedding of in ^c () yields the identity map on , and every-continuous affine transformation of can be represented by an affine transformation of ^c () that is induced by a Markov kernel. If (X, ) is a Banach space and is a closed, bounded, generating cone base inX that is contained in a hyperplane, then analogous results are obtained with respect to ^s (). Since the state spaces considered in noncommutative measure theory are cone bases and every change in time of an empirical system can be thought of as an affine transformation of the associated state space (Schrödinger picture), the existence of these representation theorems implies that the time evolution of general empirical systems can be described by dynamical concepts borrowed from classical probability theory.     

Matrix field theory for disordered local pairing superconductors with two glass order parameters and spin-flip pairbreaking processes

We derive the exact matrix field theory for a replicated grassmannian representation of a local pairing superconducting disorder ensemble including three superconducting order parameters and the spin-flip pairbreaking mechanism. Disorder is assumed to be gaussian distributed. We find by exactly solving the saddle-point equation the criterion for a vanishing gap ^–1 + ^–1 , where denotes the averaged superconducting order parameter, ^–1 the spin-flip scattering rate, and ^–1 the scattering rate corresponding to correlations of Re(–). Taken at =0, our field theory, which is exact in all orders of ^–1 , contains new terms in addition to those of theO( ^–1 ) model derived by Efetov et al. Our formulation transfers correctly to all orders the invariances of the action into symmetries of the matrix field theory. The saddle point approximation is outlined and it is shown how singular corrections to the saddle point density of states arise atE _F in a gapless superconductor. Finally singular corrections in the two particle propagator, the density correlation function and the conductivity are calculated for =0 in one loop order. It turns out that these corrections can be entirely expressed by those of the single particle density of states.     

Critical Region for Droplet Formation in the Two-Dimensional Ising Model

We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size L ² , inverse temperature > _c and overall magnetization conditioned to take the value m L ² –2m v _L , where _c ^–1 is the critical temperature, m =m () is the spontaneous magnetization and v _L is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when v _L ^3/2 L ^–2 tends to a definite limit. Specifically, we identify a dimensionless parameter , proportional to this limit, a non-trivial critical value _c and a function such that the following holds: For < _c , there are no droplets beyond log L scale, while for > _c , there is a single, Wulff-shaped droplet containing a fraction _c =2/3 of the magnetization deficit and there are no other droplets beyond the scale of log L. Moreover, and are related via a universal equation that apparently is independent of the details of the system.     

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.