Showing papers in "Annalen der Physik in 1997"
TL;DR: Nattermann et al. as discussed by the authors considered a Langevin-type Eq. which is expected to be valid close to the depinning transition of an interface in a statistically isotropic medium.
Abstract: The dynamics of a driven interface in a medium with random pinning forces is analyzed. The interface undergoes a depinning transition where the order parameter is the interface velocity v, which increases as v ∼(FFc)θ for driving forces F close to its threshold value Fc. We consider a Langevin-type Eq. which is expected to be valid close to the depinning transition of an interface in a statistically isotropic medium. By a functional renormalization group scheme the critical exponents characterizing the depinning transition are obtained to the first order in ϵ = 4 — D > 0, where D is the interface dimension. The main results were published earlier [T. Nattermann et al., J. Phys. II France 2 (1992) 1483]. Here, we present details of the perturbative calculation and of the derivation of the functional flow Eq. for the random-force correlator. The fixed point function of the correlator has a cusp singularity which is related to a finite value of the threshold Fc, similar to the mean field theory. We also present extensive numerical simulations and compare them with our analytical results for the critical exponents. For ϵ = 1 the numerical and analytical results deviate from each other by only a few percent. The deviations in lower dimensions ϵ = 2, 3 are larger and suggest that the roughness exponent is somewhat larger than the value ξ = e/3 of an interface in thermal equilibrium.
116 citations
TL;DR: In this article, the authors investigate two models for "traffic flow with modified acceleration ('slow-to-start') rules", and compare the effects of the two different slow-to start rules and discuss their relevance for real traffic.
Abstract: We investigate two models for 'traffic flow with modified acceleration ('slow-to-start') rules. Even in the simplest case w,,, = 1 these rules break the 'particle-hole' symmetry of the mod- el. We determine the fundamental diagram (flow -density relationship) using the so-called car-orient- ed mean-field approach (COMF) which yields the exact solution of the basic model with w,,,, = 1. Here we find that this is no longer true for the models with modified acceleration rules, but the re- sults are still in good agreement with simulations. We also compare the effects of the two different slow-to-start rules and discuss their relevance for real traffic. In addition, in one of these models we find a new phase transition to a completely jammed state. $8 I 11
102 citations
TL;DR: A new method of constructing cryptosystems utilising a nonpredictability property of discrete chaotic systems using a generalisation of the method presented in [7].
Abstract: In the paper we propose a new method of constructing cryptosystems utilising a nonpredictability property of discrete chaotic systems. We formulate the requirements for such systems to assure their safety. We also give examples of practical realisation of chaotic cryptosystems, using a generalisation of the method presented in [7]. The proposed algorithm of encryption and decryption is based on multiple iteration of a certain dynamical chaotic system. We assume that some part of the initial condition is a plain message. As the secret key we assume the system parameter(s) and additionally another part of the initial condition.
89 citations
TL;DR: In this paper, the authors introduce a new theoretical approach to dissipative quantum systems by means of a continuous sequence of infinitesimal unitary transformations, which decouple the small quantum system that one is interested in from its thermodynamically large environment.
Abstract: We introduce a new theoretical approach to dissipative quantum systems. By means of a continuous sequence of infinitesimal unitary transformations, we decouple the small quantum system that one is interested in from its thermodynamically large environment. This yields a trivial final transformed Hamiltonian. Dissipation enters through the observation that generically observables “decay” completely under these unitary transformations, i.e. are completely transformed into other terms. As a nontrivial example the spin–boson model is discussed in some detail. For the super–Ohmic bath we obtain a very satisfactory description of short, intermediate and long time scales at small temperatures. This can be tested from the generalized Shiba–relation that is fulfilled within numerical errors.
53 citations
TL;DR: In this article, a general method to solve the equation of motion of a vibrating SFM cantilever/tip system in an external force field is presented, which is based on the MYD/BHW model.
Abstract: In the field of Scanning Force Microscopy several dynamical contact and noncontact modes have been introduced increasing the range of detectable surface and interface properties, and allowing to detect material properties such as elasticity and mass density on the nanometer scale A detailed understanding of tip/surface interactions and the dynamic processes involved is required to understand the origin of a material contrast using these techniques Here a general method to solve the equation of motion of a vibrating SFM cantilever/tip system in an external force field is presented Contact modes as well as intermittent contact modes are discussed using a single set of equations describing the cantilever/tip motion, and by varying the size of amplitudes of the vibrating cantilever/tip system To quantitatively describe the oscillation behavior of the SFM cantilever at large amplitudes the computer simulations are based on the MYD/BHW model providing a realistic contact model with respect to the contact area, the size of the contact forces as well as the transition from repulsive to attractive forces The results are compared with the experiment and with different approaches based on analytical and numerical models
36 citations
TL;DR: In this article, the phonon-induced electron-electron interaction in a solid was studied and the effective interactions between two electrons forming a Cooper pair were calculated to second order in the electron-phonon coupling.
Abstract: We study the problem of the phonon–induced electron–electron interaction in a solid. Starting with a Hamiltonian that contains an electron–phonon interaction, we perform a similarity renormalization transformation to calculate an effective Hamiltonian. Using this transformation singularities due to degeneracies are avoided explicitely. The effective interactions are calculated to second order in the electron–phonon coupling. It is shown that the effective interaction between two electrons forming a Cooper pair is attractive in the whole parameter space. For a simple Einstein model we calculate the renormalization of the electronic energies and the critical temperature of superconductivity.
27 citations
TL;DR: In this paper, a review of optical experiments on the wetting properties of liquid 4He and molecular hydrogen is presented, and the physical mechanisms responsible for the transition between wetting and non-wetting are discussed.
Abstract: Optical experiments on the wetting properties of liquid 4He and molecular hydrogen are reviewed. Hydrogen films on noble metal surfaces serve as model systems for studying triple point wetting, a continuous transition between wetting and non-wetting. By means of optically excited surface plasmons, the adsorbed film thickness for temperatures around, and far below, the bulk melting temperature is measured, and the physical mechanisms responsible for the transition are elucidated. Possible applications for other experiments in pure and applied research are discussed. Thin films and droplets of liquid helium are studied on cesium surfaces, on which there is a first order wetting transition. Our studies concentrate on dynamical observations via surface plasmon microscopy, which provide insight into the morphology of liquid helium droplets spreading at different temperatures. Features corresponding to pinning forces, the prewetting line, and the Kosterlitz-Thouless transition are clearly observed.
22 citations
TL;DR: In this paper, the authors studied the density of states (DOS) as a function of the interaction U in the half-filled simplified Hubbard model in a magnetic field, and they showed that the DOS can be calculated exactly, and that many of its properties have an astonishingly simple form.
Abstract: We study the density of states (DOS) as a function of the interaction U in the half-filled simplified Hubbard model in a magnetic field. This model is considered on the Bethe lattice in the limit of high dimensions. We show that the DOS can be calculated exactly, and that many of its properties have an astonishingly simple form. In particular, the DOS can be investigated explicitly in the limits of weak and strong coupling and near the metal-insulator transition. E.g., we find an explicit result for the critical value Uc, at which the metal-insulator transition occurs, as a function of the magnetization. The relation between the magnetization and the magnetic field is calculated numerically. An important result is that the metal-insulator transition, occurring in the model with B = 0, is continuously connected to the metal-insulator transition in the subspace of single spin flips.
22 citations
TL;DR: In this paper, the validity of the Vlasov equation as a semi-classical approximation of time-dependent Hartree-Fock and time dependent LDA theories is explored.
Abstract: We explore the validity of the Vlasov equation as a semi-classical approximation of time-dependent Hartree-Fock and time-dependent LDA theories. We discuss the h 0 limit for the propagation of quantal wavefunctions in terms of classical densities. The h 0 limit is studied formally by means of its Wigner and Husimi phase-space representations. We consider an application to the valence electron cloud of metal clusters and show a comparison between quantal and Vlasov dynamics in this case.
21 citations
TL;DR: In this article, a method for the rapid evaluation of oscillating lattice sums for layered geometries, based on the Ewald's summation technique, was proposed, which can be applied to different types of long range interactions as well as different lattice symmetries.
Abstract: We have generalized a method for the rapid evaluation of oscillating lattice sums for layered geometries, based on the Ewald's summation technique. Different types of long range interactions as well as different lattice symmetries can be considered, in particular modulated magnetic structures, periodic domain patterns, or periodic lattice distortions. As examples the demagnetizing energies for different thin films systems and magnetic excitations in a single atomic layer are calculated.
17 citations
TL;DR: In this article, the authors provide a semiclassical description of the shell structure in large prolate cavities, using a version of Gutzwiller's trace formula that takes into account continuous symmetries.
Abstract: We provide a semiclassical description of the shell structure in large prolate cavities. Level densities and shell-correction energies are obtained from periodic orbit theory, using a version of Gutzwiller's trace formula that takes into account continuous symmetries. The semiclassical results are compared to their quantum-mechanical counterparts.
TL;DR: In this paper, the validity of the Vlasov equation as a semi-classical approximation of Hartree-Fock and time-dependent LDA theories in terms of the survival of the Pauli principle was explored from a numerical point of view.
Abstract: We explore from a numerical point of view the validity of the Vlasov equation as a semi-classical approximation of time-dependent Hartree-Fock and time-dependent LDA theories, in terms of the survival of the Pauli principle. The fermionic properties are investigated by using a Na9+ cluster as test case and solving the Vlasov equation with the test particle method. This allows to derive a time span for which the Vlasov equation provides an acceptable approximation.
TL;DR: In this paper, it was shown that 4f systems are good candidates for electron or hole crystallization to occur since the small radius of the 4f shell leads to small hybridizations and hence kinetic energy of the f electrons.
Abstract: A necessary condition for electron crystallization is the dominance of the electronic Coulomb repulsion as compared with the kinetic energy. We show that 4f systems are good candidates for electron or hole crystallization to occur since the small radius of the 4f shell leads to small hybridizations and hence kinetic energy of the f electrons. Crystallization may take place in lattices with several equivalent 4f sites per unit cell when the electron or hole number is less than the number of sites. We give evidence that charge ordering in Yb4As3 is an example of the mechanism considered here. We also compare it with those considered by Wigner, Verwey, Mott and Hubbard.
TL;DR: In this article, the authors studied the interbasis expansion of the wave functions of the Kaluza-Klein monopole system in the parabolic coordinate system with respect to the spherical coordinate system, and vice versa.
Abstract: We study the interbasis expansion of the wave-functions of the Kaluza-Klein monopole system in the parabolic coordinate system with respect to the spherical coordinate system, and vice versa. We show that the coefficients of the expansion are proportional to Clebsch-Gordan coefficients. We analyse the discrete and continuous spectrum as well, briefly discuss the feature that the (reduced) Kaluza-Klein monopole system is separable in three coordinate systems, and the fact that there are five functionally independent integrals of motion, respectively observables, a property which characterizes this system as super-integrable.
TL;DR: In this article, the decay rates for the evaporation of cluster atoms from hot liquid alkali metal clusters are derived starting from the Weisskopf theory, where the crucial input quantity is the level density which is determined from empirical properties of the bulk, namely from the specific heat and the thermal expansion coefficient.
Abstract: Starting from the Weisskopf theory decay rates for the evaporation of cluster atoms from hot liquid alkali metal clusters are derived. The crucial input quantity is the level density which is determined from empirical properties of the bulk, namely from the specific heat and the thermal expansion coefficient. The resulting rate expression is compared with decay rate formulas given by Engelking, Klots and Gspann. Furthermore, critical (appearance) sizes of multiply charged clusters are calculated by equating the rates for neutral monomer and light charged particle emission. Also shrinking and cooling rates of large hot clusters are determined by treating multiple emission of cluster atoms, thus establishing a time scale for the decay of clusters theoretically.
TL;DR: In this article, the spontaneous bulk, surface and corner magnetizations in the square lattice Ising model can all be obtained within one approach based on functional equations which follow from the properties of corner transfer matrices and vertex operators and which can be derived graphically.
Abstract: We show how the spontaneous bulk, surface and corner magnetizations in the square lattice Ising model can all be obtained within one approach. The method is based on functional equations which follow from the properties of corner transfer matrices and vertex operators and which can be derived graphically. In all cases, exact analytical expressions for general anisotropy are obtained. Known results, including several for which only numerical computation was previously possible, are verified and new results related to general anisotropy and corner angles are obtained.
TL;DR: In this paper, a Gaussian wave functional for the ground state is used to reorder the Hamiltonian into a free part with a variationally determined mass and the rest of the residual Hamiltonian can, in principle, be treated perturbatively.
Abstract: We use a Gaussian wave functional for the ground state to reorder the Hamiltonian into a free part with a variationally determined mass and the rest. Once spontaneous symmetry breaking is taken into account, the residual Hamiltonian can, in principle, be treated perturbatively. In this scheme we analyze the O(1) and O(2) scalar models. For the O(2)-theory we first explicitly calculate the massless Goldstone excitation and then show that the one-loop corrections of the effective Hamiltonian do not generate a mass.
TL;DR: In this paper, the total energies and related quantities of sequences of small clusters of the form Am Pbn, where A is an alkali atom, n < 6 and m < 9, are reported.
Abstract: Calculations are reported of the total energies and related quantities of sequences of small clusters of the form Am Pbn, where A is an alkali atom, n <6 and m < 9. The object of this study is to shed light on the stoichiometry and the possible formation of complexes in A-Pb liquid alloys. The calculations are performed using empty core pseudopotentials and the spherical average approximation for the cluster. The results are insensitive to the choice of alkali atom apart from a smooth trend with the progression from Li to Cs. The calculated total energies suggest that clusters with compositions A4Pb and A4Pb4 are very stable against a change in the number of Pb or A atoms and support the possibility of these clusters forming in the liquid alloys. This stability arises from an electronic shell-closing effect.
TL;DR: The tunneling of two lithium ion impurities on next-nearest neighbor sites in potassium chloride is investigated both experimentally and theoretically in this paper, where the strong dipolar interaction leads to coherent tunneling motion of the two defect ions between degenerate off-center positions.
Abstract: The tunneling of two lithium ion impurities on next-nearest neighbor sites in potassium chloride are investigated both experimentally and theoretically. The strong dipolar interaction leads to coherent tunneling motion of the two defect ions between degenerate off-center positions. Comparing data of rotary echo experiments for impurity pairs 7Li—7Li, 6Li—6Li, and 7Li—6Li with theory permits a thorough investigation of the isotope effect and of the effect of the interaction on the tunnel states. Our findings confirm the tunneling model with off-center states to be valid even for strongly interacting impurities. Using degenerate perturbation theory in terms of two-particle states, we obtain essentially exact expressions for the tunneling spectrum and the dynamical susceptibility which agree well with the measured data.
TL;DR: In this article, the authors investigated a polycrystalline gold layer on glass by a scanning tunneling microscope in air and found tunneling current oscillations, which are excited by the DC voltage across the gap.
Abstract: Investigating a polycrystalline gold layer on glass by a scanning tunneling microscope in air, tunneling current oscillations were found, which are excited by the DC voltage across the gap. The oscillation amplitude is dependent on the place on the surface of the sample and correlates with its topography. The frequency spectra of these oscillations are influenced by resonances of the mechanical system (z-piezo/sample holder/transducer/sample). A piezoelectric transducer is able to detect alternating forces originating from the tunnel junction. The resonances in the spectrum of the AC tunneling current and the mechanical resonances of the STM system seem to be related.
Trapping and subsequent delayed desorption of charge carriers at localized surface states could play a role in generating the observed time-dependent forces across the gap and thereby creating tunneling current oscillations.
TL;DR: In this article, the total nuclear level density is obtained for periodic single particle spectra using Jacobi theta functions for degenerated fermion systems, and a relation for the number of representations of an integer number as sums of smaller numbers is derived.
Abstract: The total nuclear level density is obtained for periodic single particle spectra. First, we express the canonical partition function in terms of Jacobi theta functions for degenerated fermion systems. Secondly, we use a relation for the number of representations of an integer number as sums of smaller numbers to find an exact formula for the nuclear level density. The shell structure is incorporated in the result in a simple way. An asymptotic relation can be easily obtained from the exact result and shown to be the well known back-shifted Bethe-formula.
TL;DR: In this paper, the electrical resistance of single crystals of the high-temperature superconductor Tl2Ba2CaCu2O8 has been measured as a function of the angle θ between the direction of the magnetic field and the current-carrying CuO2-planes.
Abstract: The electrical resistance of single crystals of the high-temperature superconductor Tl2Ba2CaCu2O8 has been measured as a function of the angle θ between the direction of the magnetic field and the current-carrying CuO2-planes. The resistance is maximal for θ = 90° (B⟂CuO2-planes) and decreases to a minimum at θ = 0°. For small angles an anomalous enhancement of the resistance is found. While the general shape of the resistance is generated by the motion of “pancake vortices” in the CuO2-planes, the anomaly is due to “Josephson vortices” moving perpendicular to the planes.
TL;DR: In this article, the Schrodinger-Pauli equation is solved numerically for spin relaxation of spin-1/2 quantum particles on linear chains with random Larmor frequencies.
Abstract: Spin relaxation of spin-1/2 quantum particles on linear chains with random Larmor frequencies is studied. Wave packets are prepared with initial spin polarization in the propagation direction and with either zero, or finite group velocity. The discrete Schrodinger-Pauli equation is solved numerically. Exponential spin relaxation is observed in a restricted time range. The decay constant depends on the width of the distribution of the Larmor frequencies and on the group velocity. No dependence on the initial halfwidth of the wave packet is found.
TL;DR: In this paper, the average magnetic moment of two-dimensional electrons in mesoscopic samples is studied in models where the interaction between electrons is neglected, and three distinct ranges in the magnetic field: (i) small field region where perturbation theory applies; (ii) moderate fields where edge currents play a prominent role; and (iii) the high field range with a Landau type susceptibility.
Abstract: The orbital magnetism of two-dimensional electrons in mesoscopic samples is studied in models where the interaction between electrons is neglected. Various geometries are considered as there are disc, plaquette, bracelet with hard wall confinement and also a confinement with a parabolic potential. We calculate the average magnetic moment which means an average with respect to size fluctuations and de Haas-van Alphen oscillations which arise in the case of a sharp Fermi cutoff. We see three distinct ranges in the magnetic field: (i) small field region where perturbation theory applies; (ii) moderate fields where edge currents play a prominent role; and (iii) the high field range with a Landau type susceptibility. In a quasiclassical picture, the electronic orbits are not qualitatively changed by a magnetic field in (i); skipping orbits are important in (ii); and in (iii), the cyclotron radius is smaller than the sample size. As a rule, we find an enhancement of the magnetic response which increases with kFL, that is, with sample size divided by the Fermi wave length. Also, we have found out that the quasiclassical approximation fails in the calculation of the magnetic properties; on the other hand, we have seen no essential differences between the canonical ensemble (fixed particle number) and the grand canonical ensemble (chemical potential given). In the case of plaquettes, in particular for samples in the form of squares, we have found agreement with experimental results by Levy, Reich, Pfeiffer and West.
TL;DR: In this paper, it was shown that the potential perturbation that shifts a chosen standing wave in space is a block of potential barrier and well for every wave bump between neighbouring knots, and that the algorithms shifting the range of the primary localization of a chosen bound state in a potential well of finite width are applicable to the scattering functions if states of the continuous spectrum are considered as bound states normalized to unity but distributed on an infinite interval with vanishing density.
Abstract: It is shown that the potential perturbation that shifts a chosen standing wave in space is a block of potential barrier and well for every wave bump between neighbouring knots. The algorithms shifting the range of the primary localization of a chosen bound state in a potential well of finite width are as well applicable to the scattering functions if states of the continuous spectrum are considered as bound states normalized to unity but distributed on an infinite interval with vanishing density. The potential perturbations of the same type on the half-axis concentrate the scattering wave at the origin, thus creating a bound state embedded into the continuous spectrum (zero width resonance).
TL;DR: In this paper, the authors considered the problem of sliding motion of a charge-density-wave subject to static disorder within an elastic medium model and proposed a self-consistent approximation scheme to obtain results beyond the standard large-velocity expansion.
Abstract: We consider the problem of sliding motion of a charge-density-wave subject to static disorder within an elastic medium model. Starting with a field-theoretical formulation, which allows exact disorder averaging, we propose a self-consistent approximation scheme to obtain results beyond the standard large-velocity expansion. Explicit calculations are carried out in three spatial dimensions. For the conductivity, we find a strong-coupling regime at electrical fields just above the pinning threshold. Phase and velocity correlation functions scale differently from the high-field regime, and static phase correlations converge to the pinned-phase behaviour. The sliding charge-density-wave is accompanied by narrow-band noise.
TL;DR: In this article, Huang and Yang replace a hard core of radius c by their pseudopotential (HYPP), which can be used in perturbation theory. And they show that HYPP and boundary value perturbance theory give the same energy shift, to first order in c.
Abstract: Huang and Yang replace a hard core of radius c by their pseudopotential (HYPP), which can be used in perturbation theory. I show that HYPP and boundary value perturbation theory give the same energy shift, to first order in c. I model a two-body potential as an oscillator potential (angular frequency ω) and a hard core. For an A-body system, the ratio of the first order energy correction to the unperturbed energy is 0.448 A3/4c a, where a = (M ω/2h)1/2.
TL;DR: In this paper, the Peccei-Quinn CP conserving mechanism of the DFSZ invisible axion model has been investigated in the presence of instanton gauge field configurations, which may behave non trivially while decreasing the temperature as a consequence of the vacuum symmetry modifications.
Abstract: During the thermal evolution of the universe, symmetry of the vacuum state in the presence of quantum fields should have changed at various stages. A possible indication of this effect on the DFSZ invisible axion model of the Peccei-Quinn CP conserving mechanism is presented here. To start with, the background theory of this mechanism in the cosmic evolution has been fully reviewed, as well as the leading cosmological arguments setting limits on the mass and coupling of such a particle. The CP conserving lagrangian of the invisible axion model also includes instanton gauge field configurations. In our opinion, these configurations could behave non trivially while decreasing the temperature as a consequence of the vacuum symmetry modifications. The interplay between symmetry modifications and cosmic evolution may thus lead to yet unclear effects. In fact, the model considered here is really quite a baby version of the real world, so that only preliminary indications and bare consistency arguments have been done from it. Nevertheless, the underlying idea, a possible neutral Higgs fields approximate resonance condition, seems to survive even in more sophisticated models.
TL;DR: In this paper, it was shown that due to vacuum polarization effects, the original bare charges of electrons and positrons are smeared out so much that their original divergent energy distances from the vacuum energy become finite.
Abstract: In a first step we have tried to show that very probably in Quantumelectrodynamics (QED) due to vacuum polarization effects the original bare charges of electrons and positrons are smeared out so much that their original divergent energy distances from the vacuum energy become finite. Furthermore, we have sketched how one has to generalize the calculations to refine the considerations presented in this paper.
TL;DR: In this article, ground state fluctuations of the spin system are invoked to change the direction of the AF order parameter within one layer relative to that in a neighboring layer, thereby permitting some tunneling.
Abstract: An ideal antiferromagnetic (AF) ordering of the spins of the CuO layers of an underdoped cuprate prevents the low energy tunneling of the charge carriers between the layers. In order to obtain a non-vanishing c-axis conductivity (σc), we invoke ground state fluctuations of the spin system. These provide a frequency-dependent gating effect by changing the direction of the AF order parameter within one layer relative to that in a neighboring layer, thereby permitting some tunneling. The calculated σc compares favorably with experimental data in a) being small and b) having a weak frequency dependence of distinctly non-Drude form.