Showing papers in "European Physical Journal B in 1980"

Inverse participation ratio in 2+ε dimensions

Abstract: The averaged moments of the eigenfunctions (including the inverse participation ratio) of a particle in a random potential are considered near the mobility edge. The exponents of the power laws are given in ane-expansion in one-loop order for ad=2+e dimensional system. The calculation is based on a recent formulation of the mobility edge problem which maps it onto a model of interacting matrices.

Disordered system withn orbitals per site: Lagrange formulation, hyperbolic symmetry, and goldstone modes

Abstract: We give a Lagrange formulation of the gauge invariantn-orbital model for disordered electronic systems recently introduced by Wegner. The derivation proceeds analytically without use of diagrams, and it identifies the previously discussedn→∞ limit as the saddle-point approximation of the Lagrangian formulation. We discover that the Lagrangian model crucially depends on the position with respect to the real axis of the energies involved. If the energies occur on both sides of the real axis as is the case in the calculation of the conductivity, then the order parameter field takes values in a set of complex non-hermitean matrices. If all energies are on the same side of the real axis then a hermitean matrix model emerges. This difference reflects a difference in the symmetries. Whereas in the latter case normal unitary symmetry holds, the symmetry in the former case is of hyperbolic nature. The corresponding symmetry group is not compact and this might be a source of singularities also in the region of localized states. Eliminating massive modes in tree approximation we derive an effective Lagrangian for the Goldstone modes. The structure of this Lagrangian resembles the non-linear σ-model and is a very general consequence of broken isotropic symmetry. We also consider the first correction to the tree approximation which is related to the invariant measure of the generalized non-linear σ-model.

A general method for the solution of nonlinear soliton and kink Schrödinger equations

Abstract: We present a method by which one-dimensional nonlinear soliton and kink Schrodinger equations can be solved in closed form. The hermitean nonlinear soliton operator may contain up to second derivatives of the wave function and the vanishing condition must hold. The method is applied to solve known nonlinear Schrodinger equations for one-soliton and one-kink solutions and, by inverting the procedure, to derive new operators with wave packet solutions of algebraic and arbitrary shapes. One of them is equivalent to the Derivative Nonlinear Schrodinger equation.

Two-dimensional ising models with competing interaction—a Monte Carlo study

Abstract: Two-dimensional Ising models on a square lattice with competing interactions along one axis or both axes are studied primarily by the Monte Carlo method. Several commensurate-incommensurate transitions are found. Dislocation-like configurations are identified near the sinusoidal — paramagnetic transition in accordance with the idea that the transition might be of Kosterlitz-Thouless, XY-like character.

Selective sublattice dilution in ordered magnetic compounds: A new kind of percolation problem

Abstract: A magnetic binary system is considered whereA-atoms andB-atoms occupy different sublattices but it is an exchangeJ AB which is responsible for magnetic ordering. Diluting such a system with nonmagnetic atoms it is natural to treat situations where the dilution probability is different for both sublattices. In particular the extreme cases, where either only theA-sublattice or only theB-sublattice is diluted, is discussed for a variety of lattice structures atT=0. It is shown that in some cases the problem can be reduced to ordinary site- or bond percolation problems, while in other cases a new kind of percolation problem arises. Particular attention is paid to the case of spinel structures, and a discussion of recent experiments on the mixed systemyMg2TiO4−(1−y)MgFe2O4 is given. It is shown that additional frustration effects due to competing interactions are necessary to explain the breakdown of magnetic order upon dilution in that material. Critical exponents for this new kind of percolation problem are also estimated by Monte-Carlo methods and it is suggested that it belongs to the same universality class as usual percolation. As a check of the numerical procedures we redetermine the percolation concentrations of both sublattices of the spinel structure, and find that some of the earlier work on this problem is rather inaccurate.

I. XPS study of 3d-metal ions dissolved in aluminium

Abstract: The core and valence band spectra of diluteAlMn,AlNi andAlCu alloys have been investigated by x-ray induced photoemission spectroscopy (XPS). The 2p levels of Mn and Cu inAlMn andAlCu change only slightly compared to their properties in the pure metals, whereas those of Ni inAlNi lose both their asymmetry and the two hole satellite. The 3s spectra of Mn inAlMn show a splitting of 2.9 eV, as compared to 4.3 eV in Mn metal. This indicates that inAlMn the Mn ion is magnetic, at least in the time scale of the XPS measurement. The valence band spectra of the alloys (and ofAlFe andAlCo) show virtual bound states with a width of about 1.5 eV and a distance relative to the Fermi energy which increases with increasingd-occupancy. The energy of the Al plasmons increase with increasingd-metal content.

Effects of spin interactions in disordered electronic systems: Loop expansions and exact relations among local gauge invariant models

Abstract: Spindependent ensembles for disordered electronic systems are examined in the region of extended states. We derive relations between spindependent and previously studied spinless ensembles. We prove that these relations are valid in all orders of a graph theory, on the basis of which we propose them to be exact. These exact relations and supplementary two loop order calculations in 2+ɛ dimensions are used to reveal the existence of universality classes for the critical behaviour at the mobility edges. The mobility edge behaviour of a spindependent ensemble with real (random) hopping agrees with that of the spinless phase invariant ensemble except for a crossover to the real matrix ensemble in the limit of vanishing spinflip amplitudes. Anomalous properties in the band center are also discussed. We derive a transformation which maps arbitrary correlation functions of a complex spindependent ensemble into those of the real matrix ensemble. This relation implies the absence of a mobility edge for the complex spindependent ensemble within the validity region of the theory.

Soft modes in semiconducting SrTiO3: II. The ferroelectric mode

Abstract: The frequency, temperature and wavevector dependence of the ferroelectric soft mode in semiconducting SrTiO3 was investigated by temperature derivative Raman spectroscopy and by inelastic neutron scattering. A tremendous shift in mode frequency with “free” electron and oxygen vacancy concentration, respectively, was observed.

Diffusion and hopping conductivity in disordered one-dimensional lattice systems

Abstract: We investigate one-dimensional lattice systems with (symmetric) nearest neighbor transfer ratesWn, n+1 which are independently distributed according to a probability densityρ(w). For two general classes ofρ(w), we rigorously determine the asymptotic behavior of the relevant single site Green function 〈\(\tilde P\)0(ω)〉 nearω=0, and obtain exact results for the long time decay of the initial probability amplitude and for the low energy density of states. A scaling hypothesis, accurately confirmed by computer simulations, is used to relate the low frequency hopping conductivityσ(ω) uniquely to 〈\(\tilde P\)0(−iω)〉, and we conjecture that the resulting asymptotic behavior forσ(ω) is also exact. The critical exponents associated with the various asymptotic laws depend onρ(w) and show a crossover from universal to non-universal behavior. Comparison is made with the results of several approximate treatments.

External non-white noise and nonequilibrium phase transitions

Abstract: Langevin equations with external non-white noise are considered. A Fokker Planck equation valid in general in first order of the correlation timeτ of the noise is derived. In some cases its validity can be extended to any value ofτ. The effect of a finiteτ in the nonequilibrium phase transitions induced by the noise is analyzed, by means of such Fokker Planck equation, in general, for the Verhulst equation under two different kind of fluctuations, and for a genetic model. It is shown that new transitions can appear and that the threshold value of the parameter can be changed.

Numerical studies on the Anderson localization problem

Abstract: Our study of Anderson's tight binding model for strongly disordered electronic systems is extended to a numerical treatment of thed c-conductivityσ atT=0. For 100 × 100 square lattices, 129 × 129 triangular lattices, and for diamond lattices with 27,000 sites, the behaviour ofσ is studied as a function of the Fermi energy and the disorder. The calculations are based on the exact eigenfunction representation of the Kubo formula, which is evaluated by the systematic application of recursion algorithms. Our results are in favour of Mott's original suggestion of a minimum metallic conductivityσ min, both in two and three dimensions. In two dimensions we find the universal value ofσ min=(0.11 ±0.02)e 2/ℏ.

The temperature dependence of rotational tunneling

Abstract: In the last few years tunneling transitions have been observed for the highly symmetric groups CH4, CD4, NH4+, and CH3 rotating in various environments. Typically the tunneling lines shift to lower energies with increasing temperatures. In this paper the shift of the tunneling energy is calculated in a microscopic approach to the problem. The coupling of the rotating groups to the lattice modes is studied in two stages. First the rotating group is coupled to a single oscillator, then to the modes of a Debye crystal. The first calculation leads to a set of discrete tunneling lines with an energy that diminishes as the oscillator is excited into higher levels. The second approach yields a single tunneling line shifted down-wards with increasing phonon population. The shiftΔ ω is proportional toT4. The calculation explains the energy shift of the tunneling lines with reasonable values for the coupling parameters. In some cases also a broadening has been observed which does not follow from our calculations.

Crystal field splitting of some rare earth intermetallic compounds with Cu3Au structure

Abstract: Inelastic neutron scattering studies were performed in the paramagnetic phases of several rare earth compounds that crystallize in the cubic Cu3Au structure: ErPb3, ErTl3, ErIn3, HoPb3, HoTl3, HoIn3, PrSn3, PrPb3, PrTl3, PrIn3, CeIn3, La1−c Pr c Tl3, and Pr(In0.5Tl0.5)3. The energies, widths and intensities of the crystal field excitations are determined and discussed in terms of interactions between the rare earth ions. Variations of the crystal field parameters are observed across the series.

Dielectric Function and Infrared Absorption of Small Metal Particles

Abstract: Using known quantum mechanical models of electrons in a box, a smoothed dielectric function is derived for an envelope taken over the discrete dipole transitions of a small metal particle. This dielectric function deviates strongly from the Drude function at low frequencies (IR) while it merges into the latter at high frequencies (visible and UV). The function is used then to show that it is not the electric but the magnetic dipole absorption due to eddy currents, contained already in the Mie scattering theory, which reproduces the small particle dielectric function in the infrared. The possibilities and limitations of experimental confirmation are discussed.

Liquid-like structure of vapour quenched SnAu- and SnCu-films

Abstract: SnAu- and SnCu-alloys are vapour quenched at cryogenic temperatures. Resistivity and electron diffraction patterns were recorded in situ. The scattered intensities have been normalized to interference functions. The overall agreement with those of the corresponding liquid systems is quite well. The average interatomic distances obtained from the atomic distribution functions show a concentration dependence which corresponds closely to that found in liquid SnAu and SnCu respectively. This gives evidence to the statement that the nearest neighbour organisations of the films are very similar to those of the corresponding liquids. Furthermore it turned out that the local structures in the Sn-rich SnAu-system are substantial different from those in the Sn-rich SnCu-system, except in the vicinity of a minimum amount of noble metals (8–10 at.%), which is necessary to stabilize the amorphous state.

Langevin description of markovian integro-differential master equations

Abstract: For a given master equation of a discontinuous irreversible Markov process, we present the derivation of stochastically equivalent Langevin equations in which the noise is either multiplicative white generalized Poisson noise or a spectrum of multiplicative white Poisson noise. In order to achieve this goal, we introduce two new stochastic integrals of the Ito type, which provide the corresponding interpretation of the Langevin equations. The relationship with other definitions for stochastic integrals is discussed. The results are elucidated by two examples of integro-master equations describing nonlinear relaxation.

Magnetic correlations in Eu x Sr1−x S and the ferromagnet-spin glass transition

Abstract: Neutron (Bragg and small angle) scattering and susceptibility measurements are used to study magnetic ordering in Eu x Sr1−xS with ferromagnetic nearest neighbor exchangeJ1 and antiferromagnetic next-nearest neighbor exchangeJ2. We present data for 0.50≦x≦0.70 which cannot be analyzed within the merely geometrical treatments of percolation theory. Breakdown of ferromagnetism occurs atx c =0.51, far above the percolation thresholdx p =0.136, and a spin-glass phase is observed in the intermediate concentration regime. Close tox c , the ferromagnetic state is also displaced by the spinglass phase at lower temperatures. Both properties are a general characteristic of diluted systems with competing interactions. An effective decoupling of finite magnetic clusters from the ferromagnetic net arises from frustration, which enhances the ground-state entropy. Anomalous properties below the Curie temperatureT c as well as atT c support this microscopic picture.

Magnetic correlations in three-dimensional ising spin glasses

Abstract: By a recursive method numerically exact free energies are calculated forL×L×M Ising lattices with random bonds andL=4, 4≦M≦10, applying free boundaries in the direction where the lattice is less small and otherwise periodic boundary conditions. Both for the±J model and the gaussian model the specific heat is in fair agreement with Monte Carlo results obtained for much larger lattices. However, the correlation function [〈S 0 S R 〉 2 ]av is found to decay exponentially with distanceR [for 1≲R≦9] at temperatures far below the apparent freezing temperatures of the Monte Carlo simulations, implying that there is no nonzero Edwards-Anderson order parameter in equilibrium. This behavior is qualitatively different from Mattis spin glasses (or Ising ferromagnets) where even smaller lattices show pronounced magnetic order at low temperatures. As the Monte Carlo results give evidence for a nonzero Edwards-Anderson order parameter (for not too long observation times), which is fairly independent of lattice size down to sizes of 43, we suggest that Edwards-Anderson ordering is a nonequilibrium phenomenon visible only in studying dynamic properties.

The Interface in a Ginsburg-Landau-Wilson Model: Derivation of the Drumhead Model in the Low-Temperature Limit

Abstract: The drumhead model for a (d—1)-dimensional interface between two coexisting thermodynamic phases is derived from ad-dimensional one-component Ginsburg-Landau-Wilson model in the low-temperature limit. This is done by expanding about the appropriate mean-field solution, the kink, and using the kink position as a collective coordinate.

Optical properties of dense exciton-biexciton systems

Abstract: We investigate in the framework of the dielectric formalism the anomalies which have been observed in high intensity excitonic polariton-polariton scattering experiments. The anomalies are due to the virtual formation of biexcitons. Our results are in quantitative agreement with the experimental observations of Itoh et al. for CuCl.

II. XPS study of 3d-metal ions dissolved in noble metals

Abstract: Valence and core level spectra ofAgMn,AuFe,AuCo,AuNi,CuFe,CuCo andCuNi will be reported. Clearly defined virtual bound states (vbs) can only be detected in the spin fluctuating systemsAuNi andCuNi. An increase in the density of states near the Fermi energy, in the region of the flats-p band of the host metal is observed in the other magnetic alloys. There are indications that a large hybridization between the impurity and the host metald-electrons exist. The impurity core levels show satellites. They can originate from the emission from real isolated impurities and from many body effects.

A note on the diagonalization of quadratic boson and fermion hamiltonians

Abstract: We take advantage of the symmetry present in quadratic boson and fermion hamiltonians to give a short and simple derivation of their diagonalizations. This is of particular relevance to bosons. Both procedures are critically evaluated and a striking resemblance is pointed out.

Universality classes for one dimensional kinetic Ising models

Abstract: We use variational techniques to construct upper and lower bounds for the dynamical exponentz of kinetic Ising models. The most important universality class is shown to havez=2. We find larger values ofz, however, for continuous sets of both pure single-spin-flip and double-spin-flip models. For pure double-spin flips with order parameter conservation we findz≧5; this bound is consistent with a corresponding transport coefficient which vanishes at the zero-temperature critical point.

Solution of Fokker Planck equations with and without manifest detailed balance

Abstract: Previous work on Fokker Planck equations with manifest detailed balance is generalized to include also the case without manifest detailed balance. The two cases are unified by exhibiting a general time reversal transformation with respect to which any Fokker Planck equation satisfies detailed balance, provided its steady state distribution exists. We also introduce a new method for solving some Fokker Planck equations with nonvanishing steady state drift by analytic continuation of the solution of a hermitian eigenvalue problem.

Localized dynamic perturbations in metals

Abstract: The effect of a localized time-dependent potential on a Fermi gas is discussed. We introduce a new procedure to describe the excitation spectrum in terms of bosons, which is valid also for large perturbations. This is confirmed by a comparison with a fermion calculation for perturbations that vary slowly in time.

Analytic description of optical bistability including spatial effects

Abstract: Steady-state features for both absorptive and dispersive bistability are obtained analytically with the inclusion of spatial effects. Both Fabry-Perot and ring-cavity geometries are treated using an analytic integration of coupled field equations for counter-propagating waves in a homogeneously broadened two-level medium. The mean-field limit is rigorously introduced starting from exact solutions. Mean-field state equations for both Fabry-Perot and ring cavities are obtained. In the former case explicit comparisons are made with results arising in the approximate treatment of standing waves.

Solutions and applications of tridiagonal vector recurrence relations

Abstract: The applications of infinite systems of linear first order differential equations with 2L+1-term recursion formulas are discussed. It is shown that such systems can be written as a system of linear tridiagonal vector equations of dimensionL. A general method is presented by which the initial value problem can be solved by iteration. For special but physically important initial conditions the solution is given by a matrix continued fraction. The eigenvalues of the tridiagonal vector recurrence relations are obtained as the roots of aL×L determinant the elements of which are determined by a matrix continued fraction. The applicability of the method is demonstrated by calculating the eigenvalues of the laser Fokker-Planck operator.

A direct renormalization group approach for the excluded volume problem

Abstract: We propose a position-space renormalization group approach for the excluded volume problem in a square lattice by considering “percolating” self-avoiding paths in ab×b cell, whereb=2,3,4: Two ways of counting the paths are presented. The values obtained for the exponentv converge respectively to 0.731 and 0.720, close to the usually accepted valuev=0.75. Comments on the relation between percolation and self-avoiding walks are made.

Structural and magnetic phase transitions in TbPO4 studied by neutron diffraction

Abstract: Neutron diffraction experiments on TbPO4 single crystals have been performed in the temperature range from 1.35 to 294 K. We observe two phase transitions: the onset of antiferromagnetic ordering along the tetragonalc-axis at 2.28 K and tilting of the moments away from thec-axis below 2.15 K. The analysis of the measured reflection profiles shows that the tilting is connected with a distortion of the tetragonal zircon structure.

LaAg x In 1- x

Abstract: The phonon dispersion of LaAg x In1−x (x=1, 0.89, 0.8) has been studied by inelastic neutron scattering in the cubic high temperature phase. A soft mode behaviour was observed at theM-point. The doubling and the cubic to tetragonal deformation of the elementary cell was observed through the phase transition. The measurements of the elastic constants were extended to 450 K and their magnetic field dependence was investigated.