Showing papers in "Annalen der Physik in 1994"

Flow-equations for Hamiltonians

Abstract: Flow-equations are introduced in order to bring Hamiltonians closer to diagonalization It is characteristic for these equations that matrix-elements between degenerate or almost degenerate states do not decay or decay very slowly In order to understand different types of physical systems in this framework it is probably necessary to classify various types of these degeneracies and to investigate the corresponding physical behavior In general these equations generate many-particle interactions However, for an n-orbital model the equations for the two-particle interaction are closed in the limit of large n Solutions of these equations for a one-dimensional model are considered There appear convergency problems, which are removed, if instead of diagonalization only a block-diagonalization into blocks with the same number of quasiparticles is performed

Fulde-Ferrell-Larkin-Ovchinnikov state in layered superconductors

Abstract: The phase diagram of a layered superconductor in a large parallel magnetic field is calculated. This includes a calculation of the lower critical field beyond which the superconductor is in the FFLO-state and possesses a spatially modulated order parameter and spin polarization. The order parameter, spin polarization, free-energy density, and phase boundaries of this unconventional superconducting phase are evaluated numerically in the complete B–T plane. The analysis suggests that the transition at the lower critical field is of second order, and not of first order, as previously assumed. The order parameter of the FFLO-state merges continuously into the uniform superconducting state.

Dielectric dispersion of ferroelectric ceramics and single crystals at microwave frequencies

Abstract: The dielectric constant of ferroelectric ceramics shows strong Debye-like relaxation at GHz frequencies. This relaxation is caused by sound generation inside the crystallites. The ferroelastic domain walls which vibrate in the electric ac field are very effective shear wave transducers. The shear wave emission has a maximum when the wavelength of the sound wave is comparable to the width of the domains. Above this frequency the domain walls can no longer vibrate due to inertia and do not contribute to the dielectric constant. The observed dependence of the microwave dispersion on temperature, doping and grain size of the ferroelectric ceramic is in good agreement with the proposed mechanism of the emission of acoustic shear waves.

Towards a theory of the integer quantum Hall transition: From the nonlinear sigma model to superspin chains

Abstract: A careful study of the supersymmetric version of Pruisken's nonlinear σ model for the integer quantum Hall effect is presented. The lattice regularized model is cast in Hamiltonian form by taking the anisotropic limit and interpreting the topological density as an alternating sum of Wess Zumino terms. It is argued that the relevant large-scale physics of the model is preserved by projection of the quantum Hamiltonian on its sector of degenerate strong-coupling ground states. For values of the Hall conductivity close to e2/2h (mod e2/h), where a delocalization transition occurs, this yields the Hamiltonian of a quantum superspin chain which is closely related to an anisotropic version of the Chalker-Coddington model. The relation implies that the ratio of magnetic length over potential correlation length is an irrelevant parameter at the transition. The superspin chain resembles a 1 d isotropic antiferromagnet with spin 1/2. It has an alternating structure which however permits an invariance under translation by one site. The conductance coefficients of a quantum Hall system with N small contacts translate into N-superspin correlation functions which are governed by conformal invariance. The superspin formalism provides a framework for studying the crossover from classical to quantum percolation. It does not however encompass the frequency-dependent correlations of wave amplitudes at criticality.

Response of a Bloch oscillator to a THz-field

Abstract: In this paper we report on the observation of response of a Bloch oscillator at room temperature to a THz-field of a frequency larger than the Bloch frequency. The oscillator consisted of a semiconductor superlattice structure, with an applied dc voltage giving rise to a dc electron drift current. Submitting the oscillator to a field at a frequency of 3.3 THz caused a sizeable reduction of the current; the THz-field was generated by use of intense THz-radiation pulses focused on an antenna coupled to the superlattice. We attribute the THz-field induced reduction of the current to a frequency modulation of the Bloch oscillations of electrons at the frequency of the THz-field, leading to reduction of the electron drift velocity and, consequently, of the current.

Atomic force microscopy at MHz frequencies

Abstract: Cantilevers of atomic force microscopes usually have spring constants of less than 1 N/m and fundamental resonance frequencies for free vibration between 10 and 100 kHz. If, however, the tip is in contact with the surface of a sample vibrating at MHz frequencies, we have observed that the cantilever can be forced to vibrate also at these high frequencies with high amplitude. For the detection of the high frequency vibrations of the cantilever we added in our experiment a fast optical knife-edge detector to a commercial Atomic Force Microscope. Ultrasonic pulses were excited by a piezoelectric transducer bonded to the sample and the ultrasonic signals transmitted to the cantilever were recorded. Furthermore, the vibrational amplitude of the cantilever was measured locally along the cantilever. For comparison we also measured the absolute surface amplitude by a Michelson-heterodyne interferometer. The spectral components of the cantilever vibration were examined and discussed theoretically.

Low frequency acoustic and dielectric measurements on glasses

Abstract: The acoustic and dielectric properties of different glasses at audio frequencies and temperatures below 1 K have been investigated with the vibrating reed and a capacitance bridge technique We found the temperature dependence of the absorption of vitreous silica (Suprasil W) to agree with the predictions of the tunneling model which is commonly used to explain the low temperature behaviour of amorphous materials The variation of the sound velocity and of the dielectric constant, however, shows significant deviations from the expected behaviour which cannot be accounted for by a simple modification of the model Instead, it seems to be necessary to introduce a temperature dependence of some relevant model parameters Moreover, at very low temperatures (T < 01 K) the sound velocity strongly depends on the excitation levels The absence of this effect at higher temperatures proves that it can be ascribed to a nonlinear response of tunneling systems Similar results were found in sound velocity measurements on a cover glass and on a superconducting metallic glass (Pd30Zr70, Tc = 26 K), which indicates that these features are a general aspect of the dynamics of tunneling states in glasses In contrast to the insulating glasses we found that in Pd30Zr70 also the internal friction is strain dependent

A finite size scaling study of the five-dimensional Ising model

Abstract: For systems above the marginal dimension d*, where mean field theory starts to become valid, such as Ising models in d = 5 for which d* = 4, hyperscaling is invalid and hence it was suggested that finite size scaling is not ruled by the correlation length ξ (∝ |t| −1/2 in Landau theory, t being the distance from the critical point) but by a “thermodynamic length” l (∝ |t| −2/d). Early simulation work by Binder et al. using nearest neighbor hypercubic L5 lattices with L ⩽ 7 yielded some evidence for this prediction, but the renormalized coupling constant gL = −3 + 〈M4〉/〈M2〉2 at Tc was gL ≈ −1.0 instead of the prediction of Brezin and Zinn-Justin, gL(Tc) = −3 + Γ4(1/4)/(8 π2) ≈ −0.812. In the present work, we try to shed light on this controversy obtaining much more precise Monte Carlo data using multihistogram techniques and lattices as large as L = 17 (i.e., 1419857 Ising spins). While our value of Tc agrees nicely with recent high temperature series work (KBTc/J ≈ 8.7774 ± 0.0035), the coupling at Tc {gL(Tc) ≈ −0.958 ± 0.050} confirms the work for small lattices and disagrees with the analytical prediction. Hence the data are better consistent with a shift of the effective critical temperature Tc(L) - Tc(∝) ∝ L−d/2 rather than with L−(d−2) according to the analytical theory. If the latter behavior is correct, it can hence be seen for extremely large systems only.

Dirac particle, gravity, and inertial effects

Abstract: Dirac's equation with gravity for a noninertial observer is derived using local coordinate methods. Calculations for the equation are carried out to second order in the local coordinates. For easy application to interference experiments, the Schrodinger form of the Dirac equation with a well defined Hamiltonian in the local coordinates is presented. The presence of gravitational weighting factors in the scalar product lead to hermitian and antihermitian sectors for the Hamiltonian. The antihermitian part depends directly on the curvature and vanishes for zero curvature. The hermitian part which is important for the determination of phases is studied in detail and the nonrelativistic case is obtained by the application of three successive Foldy-Wouthuysen transformations. The results also give local currents and interactions which have pure inertial, pure gravity and mixed sectors. The pure inertial terms are the ones obtained by Hehl and Ni. The pure gravity and mixed sectors have contributions which are electric, magnetic and double magnetic in character. The focus is on the curvature contributions. Some are well within reach of the anticipated accuracy of atomic interferometers currently under consideration and other terms may follow if improvements can be made.

Spheroidally deformed sodium clusters in the selfconsistent jellium model

Abstract: We present the first systematic study of potential energy curves and prolate-oblate shape transitions of sodium clusters with 8 < N< 40 atoms. The Kohn-Sham equations are solved in the local density approximation for the jellium model with spheroidal deformations. The ionic background den- sity is taken to have a diffuse surface of Woods-Saxon type. The quadrupole and hexadecupole moments of the electron and jellium densities are investigated, revealing a strong hexadecupole dependence for selected clusters. Collective dipole resonances are described in the simple surface plasmon model. Shape transitions are found to occur at particle numbers 12- 14 (prolate-oblate), 18 -20-22 (oblate-spherical-prolate) and 30-32 (prolate-oblate), which are in good agreement with experimental results; triaxiality is predicted for Na-36. Comparing our results with those of molecular dynamics calculations, we confirm the scheme of Kohn-Sham levels and the gross behaviour of poten- tials and densities.

Bound states and superfluidity in strongly coupled Fermion systems

Abstract: The crossover from Bardeen-Cooper-Schrieffer pairing to Bose-Einstein condensation is considered with special emphasis to a consistent description of bound pair formation. A nonequilibrium approach is considered, and wave equations for the two-particle states and the pair amplitude are derived in the stationary state. The critical temperature is calculated for a simple model system.

Scanning tunneling microscopy of RF oscillating surfaces

Abstract: Amplitude and phase of high frequency surface acoustic wave (SAW) fields are investigated by a novel scanning tunneling microscopy technique. The gap voltage is modulated at a slightly detuned high frequency. Due to the nonlinearity of the tunneling process a frequency mixing appears. For scanned areas with dimensions much smaller than the wavelength of the SAW a remarkable local variation of amplitude and phase of the tunneling current at the difference frequency is observed. Depending on the local morphology different components of the particle displacement vector are detected. Model calculations of amplitude and phase images are presented for a real topography.

Electrons with correlated hopping interaction in one dimension

Abstract: The 1D system of correlated electrons characterized in addition to the usual on-site (U) and nearest-neighbour (V) repulsion by a correlated-hopping term (t*) is considered. The ground state phase diagram is studied within the framework of the weak-coupling continuum-limit approach. At filling v the effective interaction originating from the correlated-hopping term which appears in the continuum-limit theory is given by t* cos (πv). Being repulsive for v 1/2, this interaction leads to a characteristic band-filling dependence of the phase diagram of the system. For v ≠ 1/2, depending on the relation between the bare values of the coupling constants (U, V, t* cos (π v)) and, hence, on the band-filling, the system shows three different phases in the infrared limit: a Luttinger metal, a nonmagnetic metal and a singlet superconducting phase. For v = 1/2, the correlated-hopping interaction is dynamically trivial, leading only to a renormalization of the oneelectron hopping amplitude and the phase diagram of the model coincides with that of the extended Hubbard model.

A self‐consistent cluster study of the Emery model

Abstract: We calculate Fermi-surface properties of the Cuprate superconductors within the three- band Hubbard model (also called the Emery model) using a cluster expansion for the proper self- energy The Fermi-surface topology is in agreement with angular-resolved photoemission data for dop- ings - 20% We discuss possible violations of the Luttinger sum-rule for smaller dopings and the role of van-Hove singularities in the density of states of the Zhang-Rice singlets We calculate the shift in the chemical potential upon doping and find quantitative agreement with recent experiments

Path integrals for two- and three-dimensional δ-function perturbations

Abstract: The incorporation of two- and three-dimensional $\delta$-function perturbations into the path-integral formalism is discussed. In contrast to the one-dimensional case, a regularization procedure is needed due to the divergence of the Green-function $G~{(V)}(\vec x,\vec y;E)$, ($\vec x,\vec y\in\bbbr~2,\bbbr~3$) for $\vec x=\vec y$, corresponding to a potential problem $V(\vec x)$. The known procedure to define proper self-adjoint extensions for Hamiltonians with deficiency indices can be used to regularize the path integral, giving a perturbative approach for $\delta$-function perturbations in two and three dimensions in the context of path integrals. Several examples illustrate the formalism. abstract

Light scattering and small angle neutron scattering experiments with an aggregating binary liquid mixture of critical composition

Abstract: Results of light scattering and small angle neutron scattering experiments with a 2-butoxyethanol (2-C4E1)/D2O mixture of critical composition (stoichiometric mole fraction of 2-C4E1x = 00598; critical temperature Tc (visual) = 42714 °C) are reported They are carried out with the aim to find out whether the temperature dependence of the correlation length ξ characterizing the extension of concentration fluctuations near Tc is different from that characterizing the size of aggregates of the 2-C4E1 molecules which appear to exist at temperatures away from Tc The experiments show that the temperature dependence of ξ near Tc is the same as that away from Tc within the uncertainty of the measurements – As a by-product of this study, neutron scattering data were collected corresponding to a wide range of values of the scaling variable x (3 < x < 2100; x = qξ q is the absolute value of the scattering vector) They are analysed in terms of the limiting form of the universal correlation scaling function gξ(x) = C1x−(2-η) to determine the value of the universal critical exponent η A value of η = 0039 ± 0004 is found It is considered consistent with the theoretically expected values

Solutions for the T = 0 quantum spin glass transition in a metallic model with spin‐charge coupling

Abstract: We solve several low temperature problems of an infinite range metallic spin glass model. A compensation problem of T 0 divergencies is solved for the free energy which helped to extract the quantum critical behaviour of the spin glass order parameters as a function of δJ = J – Jc (T = 0). The critical value Jc(T = 0) = 3/16pF−1 of the frustrated spin coupling J, which separates spin glass from nonmagnetic (spin liquid) phase, is determined exactly in the static saddle point solution for a semielliptic metallic band model in terms of the density of states at the Fermi level. In addition to the replica-overlap order parameter 〈Qab〉, a ≠ b, the diagonal 〈Qaa〉 is confirmed as order parameter by the result 〈Qaa〉 SP ∼ (δJ)β, β = 1, and its susceptibility χaaaa ∼(-δJ)−γ with γ = 1/2 at T = 0. The value for γ agrees with the one for the transverse field Ising spin glass. The low γ decay of 〈Qaa〉, ∼ T is obtained exactly in the whole quantum disordered phase including the critical value.

Noises generated by nonlinear autoregression

Abstract: A nonlinear generalization of autoregressive scheme of first order is suggested as approximate model for 1/fk noises. The iterative generation makes use of reducing function instead of a constant. Computer simulations – carried out over three decades of frequency – have demonstrated that there is such a family of these functions that to any function of the family there exists a unique value of standard deviation of white noise source such that the noise generated by the iterative scheme has the spectral factor k ≈ 1. Implications of the results for understanding the origin, structural stability and ubiquity of 1/f noise are discussed.

Peltier‐effect in the mixed state of (Bi, Pb)2Sr2Ca2Cu3Oδ

Abstract: We present measurements of the Peltier-effect in the mixed state of Bi1.76Pb0.24Sr2Ca2Cu3Oδ. The Peltier-coefficient broadens in a magnetic field quite similar to the resistivity and the thermopower. Comparison with the thermopower shows that Onsagers relation holds well. The occurrence of the Peltier-heat in the mixed state well below Tc implies that the electric current is accompanied by a large heat current. We show that the vortex contribution to the Peltier-heat is negligibly small. Therefore the heat current has to be attributed to normal quasiparticle excitations. Our results indicate that this quasiparticle contribution to the heat current remains large even at temperatures far below Tc.

Complex conductivity in high-Tc single crystal superconductors

Abstract: The electromagnetic surface impedance of single crystal high-T c superconductors has been examined within the framework of the two-fluid model and the hypothesis that the em field modulates the partial concentrations of both normal and condensate fluids. A comparison with experimental data is reported

Electrons with alternating on-site and correlated hopping interactions

Abstract: The 1 D one-band Hubbard model with different repulsive on-site interactions on even (U+V > 0) and odd (U-V > 0) sites, supplemented by the correlated-hopping term (t* > 0), describing the modification of the electron hopping by the presence of other particles on the sites, is considered as a 1 D model for CuO systems. The ground state phase diagram is studied within the framework of the bosonization technique and renormalization group analysis valid for weak coupling. Depending on the choice of model parameters, the following sequences of phase transitions with increasing bandfilling occur: 1) metal-insulator-metal (for t* ⩽ U/4); 2) metal-insulator-metal-superconductor metal-superconductor-metal-insulator-metal-superconductor metal-superconductor .

Quark‐gluon plasma formation in heavy‐ion collision

Abstract: To account for the non-equilibrium character of quark-gluon plasma formation in relativistic heavy-ion collisions, it is proposed to use the product of energy density ϵ and interaction time τint (rather than ϵ) as the critical quantity for plasma formation. In a geometrical model, τ is approximated by the transit time, and ϵ by the maximum energy density calculated in the center-of-mass frame. For central collisions, an analytical expression for ϵ·τ is given. As an example, the systems 16O + 16O and 208Pb + 208Pb are investigated as functions of c.m. energy, and their respective suitability for plasma formation is discussed.

Electrons in a strong magnetic field on a disk

Abstract: The problem of interacting electrons moving under the influence of a strong magnetic field in two dimensions on a finite disk is reconsidered. First, the results of exact diagonalizations for up to N = 9 electrons for Coulomb as well as for a short-range interaction are used in the search for a peculiar ground state corresponding to filling factor 1/3. Not for the Coulomb, but only for the short-range interaction, can the 1/3-state be safely identified amongst the spectra of various filling factors close to 1/3. Second, the propositions of the concept of quasiparticles, as used in the hierarchical theory, are examined in view of the exact results for the disk geometry. Whereas the theory for the quasiholes is in complete accordance with the spectra, for the quasielectrons, finite size corrections make an analysis difficult. For the quasielectron energy, an extrapolation to N ∞ is given and compared with the corresponding extrapolations of three different proposals for trial wave functions. While the limiting value for the best trial wave function is very close to the limit of the exact results, the behavior of the finite size corrections of the exact energies and of the trial wave functions, respectively, is qualitatively rather different.

Vacuum Kerr-Schild metrics generated by nontwisting congruences

Abstract: The Kerr-Schild pencil of metrics gab = gab + Vlalb, with gab and gab satisfying the vacuum Einstein equations, is investigated in the case when the null vector l has vanishing twist. This class of Kerr-Schild metrics contains two solutions: the Kasner metric and a metric which can be obtained from the Kasner metric by a complex coordinate transformation. Both are limiting cases of the Kota-Perjes metrics. The base space-time is a pp-wave.

Radiation damping in closed expanding universes

Abstract: The dynamics of a coupled model (harmonic oscillator-relativistic scalar field) in Conformal Robertson-Walker (k = +1) spacetimes is investigated. The exact radiation-reaction equation of the source-including the retarded radiation terms due to the closed space geometry – is obtained and analyzed. A suitable family of Lyapunov functions is constructed to show that, if the spacetime expands monotonely, then the source's energy damps. A numerical simulation of this equation for expanding Universes, with and without Future Event Horizon, is performed.

Cluster radioactivities of odd-mass nuclei

Abstract: The partial half-lives of the hypothetical even-even equivalent of an odd-mass nucleus for cluster transitions toward various excited states of the daughter, used as a reference to find the hindrance factor, can be calculated within analytical superasymmetric fission model, by taking into account the angular momentum of the emitted cluster. Detailed tables are presented for 14 C radio-activity of 221 Fr, 221,223 Ra, 225 Ac; 24 Ne radioactivity of 233 U, 231 Pa, and 23 F decay of 231 Pa, showing that, except for 225 Ac, the existing experimental evidences, do not exclude (moderate) hindered transitions to the ground states of the daugther nuclei

Relaxation of translational energy in binary mixtures of dense hard sphere systems

Abstract: Starting from the Enskog equation we derive an analytical equation for the relaxation time necessary for the equilibration between translational energies of the components in a dense binary mixture of hard spheres. Also we give an expression for the collision number describing the average number of collisions of one particle during the relaxation time. The analytical expressions are verified by molecular dynamics simulations for various values of the packing fraction. The results are shown to be valid even for very dense systems, i.e. for liquids in the ranges of density corresponding to the freezing point. Ausgehend von der Enskoggleichung wird ein analytischer Ausdruck fur die Relaxationszeit hergeleitet, die fur den Ausgleich der Translationsenergien der Komponenten eines binaren Hartkugelgemischs hoher Dichte notig ist. Auch ein Ausdruck fur die mittlere Zahl der Stose eines Teilchens wahrend dieser Relaxationszeit wird angegeben. Die analytischen Resultate werden durch molekulardynamische Simulationsrechnungen verifiziert. Es zeigt sich, das die Ergebnisse bis in den Bereich des Phasenuberganges zum Festkorper gultig sind.

Electronic transport time through mesoscopic devices with contact barriers

Abstract: Information about the transport time of electrons through a quasi one-dimensional sample is obtained by calculating the energy auto-correlation function of the conductance. Depending on the length of the sample and its coupling to the external device (here modelled by perfectly conducting leads), the transport time undergoes a smooth crossover between two different limiting regimes. In the case of long samples and good coupling it coincides with the diffusion time. In the opposite limit of short and weakly coupled systems, however, the transport time is given by the reciprocal of the quantum mechanical decay width into the leads. The transition between both regimes is discussed in terms of a few model independent concepts.

Influence of the Ca:Pb ratio on the superconducting properties of Bi-based ceramics of type 2223

Abstract: From a study of the influence of the Ca: Pb ratio on the superconducting properties of Bi-based ceramics of 2223 type it follows that as a second parameter the employed gas atmosphere must be taken into consideration. In case of air preparation good intragrain and intergrain properties are obtained for Ca rich samples (e.g. Bi 1.8 Pb 0.2 Sr 1.9 Ca 2.1 Cu 3 O z ); whereas for Pb rich materials (e.g. Bi 1.7 Pb 0.5 Sr 1.9 Ca 1.9 Cu 3 O z ) improved conditions are encountered by employment of an Ar/O 2 (8%) atmosphere during synthesis. Independently, the transition temperature is situated near 108 K

Calculated effects of charge fluctuations on the phonon dispersion of YBa2Cu3O6 and YBa2Cu3O7. I. The model

Abstract: Using the model presented in the preceding paper we investigate the effects of charge fluctuations (CF) on the phonon dispersion of YBa2Cu3O6 (O6) and YBa2Cu3O7 (O7). Starting from an ab-initio rigid-ion model as a reference system, CF are allowed for at the copper- and oxygen ions. The CF are treated as adiabatic electronic degrees of freedom. Within the rigid-ion model (RIM) the structural parameters are calculated by minimization of the energy. The results agree reasonably well with the experiment, indicating the suitability of the ionic model as a starting point and the importance of ionic forces for the properties of the high-temperature superconductors (HTSC) in general. Next, the phonon dispersion is calculated in the RIM as well as including CF additionally and the renormalization of the individual modes is discussed. By restricting the CF optionally to the planes, effects arising specifically from CF in the planes on the one hand and from CF in the chain as well as at the axial bridging oxygens (O4) on the other hand can be separated. We find the oxygen axial modes at the γ- and Z point (A1g/A2μ in O6, Ag/B1μ in O7) particularly interesting. Most of these modes show considerable renormalizations. Moreover, the γ/Z-axial modes are characterized by the possibility of having CF of the same sign in the whole CuO planes what distinguishes them from the modes at other symmetry points. In particular, the Z-point axial modes are singular in having CF of alternating sign in consecutive structural units in c direction. Such a “c-direction-charge-transfer” has been shown previously to be an effective screening mechanism in La2CuO4. Indeed, we find a drastic renormalization of the plane-oxygen Ag mode at the Z point (Ag(O23;Z)) in O7 (oxygen ions in neighboring planes vibrating in-phase), at least in the adiabatic approximation used here. In the insulating phase this mode exhibits, on the other hand, very large changes of the potential at the ion sites, whereas its renormalization is moderate only. The reason for this behaviour is that in the insulating phase in case of a two-dimensional electronic structure the charge transfer (screening) is restricted locally in the structural unit and long-range charge transfer is not possible as in the metal. However, a strong suppression of screening for this mode can also be expected for the metallic phase in O7 in case non-adiabatic electron-phonon coupling would be important. The Ag (O23;Z)-mode thus seems to be by far the most interesting mode in O7. These features are directly related to the layered structure of the HTSC compounds considered here. The O4-axial-breathing modes show significant renormalizations too, and are characterized by plane-chain charge transfer. Moreover, besides the O23- and O4-modes, the yttrium modes appear to be important too. In addition to the phonon-dispersion curves, we present values for the CF amplitudes and screened site-potential changes at the copper-and oxygen ions. Finally, we give transverse effective charges and dielectric constants for the insulating phase (O6) as calculated within our formalism.