Structure of the Yang-Mills vacuum in the Coulomb gauge

The non-uniqueness of Yang-Mills potential in the Coulomb gauge leads to a non-trivial vacuum structure featuring vacuum fields of both integer and half-integer topological charge. Instantons fit in consistently with this picture and their interpretation is not charged. Integer and half-integer vacua are connected by certain meron solutions and the existence of half-integer charged states appears to be important for the confinement properties of the theory.     

Correlation dynamics of Yukawa-theory in 1+1 dimensions

Abstact: Using the method of correlation dynamics we investigate the properties of a field-theory for fermions and scalar bosons coupled via a Yukawa interaction. Within this approach, which consists in an expansion of full equal-time Green functions into connected equal-time Green functions and a corresponding truncation of the hierarchy of equations of motion we carry out calculations up to 4th order in the connected Green functions and evaluate the effective potential of the theory in 1+1 dimensions on a torus. Comparing the different approximations we find a strong influence of the connected 4-point functions on the properties of the system. Received: 8 January 1998 / Revised version: 7 April 1998     

Zero-conductance resonances due to flux states in nanographite ribbon junctions

Electronic transport properties through junctions in nanographite ribbons are investigated using the Landauer approach. In the low-energy regime ribbons with zigzag boundary have a single conducting channel of edge states. The conductance as a function of the chemical potential shows a rich structure with sharp dips of zero conductance. Each zero-conductance resonance is connected with a resonant state which can be interpreted as the superposition of two degenerate flux states with Kekule-like current patterns. These zero-conductance dips are connected with a pronounced negative magnetoresistance.     

Two Interfering Effects in Optogalvanic Detector Hollow Cathode Discharge

Two effects in optogalvanic detector—hollow cathode discharge are reported. They appear at light irradiation of the detector and interfere with its properties. First effect, connected with Penning process in Ar-Cd plasma, is used for identification of negative plasma resistance. The other effect is a light induced potential on the cathode.     

Investigations of backscattering peaks and of the nature of the confining potential in open quantum dots

The properties of open quantum dots are examined in magneto-transport. The quantum dots are prepared from a two-dimensional electron system (2DES) in AlGaAs/GaAs by lateral gate structures. These quantum dots are open, i.e. they are still connected to the surrounding 2DES regions. The low magnetic field magnetoresistance shows peak structures. These structures can be related to semi-classical ballistic trajectories in the confining potential of a dot. The calculations of different confining potentials (abrupt “hard-wall” and parabolic “soft-wall”) are compared with the experimental results. The experiments are better described by a soft-wall potential.     

Pseudopotential approach to magnetic energy bandstructure and magnetic breakdown in metals

The orthogonalized plane wave method of energy bandstructure calculation is generalized to the case of a metal under the influence of an external de magnetic field, with the magnetic translational symmetry taken into account fully. The magnetic field-dependent effective lattice potential or pseudopotential derived from it is interpreted as a “magnetic” pseudopotential and shown to depend only weakly on the magnetic field strength so that, to a good approximation, it can be replaced by an ordinary pseudopotential, and treated as a perturbation in the calculation of magnetic energy bands and galvanomagnetic properties in nearly-free-electron metals. Physical properties connected with the phenomenon of magnetic breakdown, in particular the Landau level broadening, which were previously shown by Pippard, Zak and others to be proportional to an unspecified pseudopotential, are reformulated in terms of the magnetic pseudopotential. The convergence of the method is also discussed.     

Equivalent circuit of the barrier-conductor structures

Novel heterostructure devices are comprised of potential barriers connected by short conductors. In this paper we present a simple theory for the transport properties of the barrier-conductor chain. The analysis is based on the solution of the Boltzmann equation supplemented by the boundary conditions provided by the barrier reflection and transmission probabilities. As an application of the theory the small signal equivalent circuit is constructed for the single and double barrier cases and for the infinite periodic chain. The high frequency properties of these structures are discussed. In general, the multibarrier structures show transit time resonances associated with multiple reflections.     

Scaling properties for a classical particle in a time-dependent potential well

Some scaling properties for a classical particle interacting with a time-dependent square-well potential are studied. The corresponding dynamics is obtained by use of a two-dimensional nonlinear area-preserving map. We describe dynamics within the chaotic sea by use of a scaling function for the variance of the average energy, thereby demonstrating that the critical exponents are connected by an analytic relationship.     

Fluctuations and stability of stationary non-equilibrium systems in detailed balance

A generalized thermodynamic potential for Markoffian systems with detailed balance and far from thermal equilibrium has been derived in a previous paper. It was shown that the principle of detailed balance is equivalent to a set of conditions fulfilled by this potential (“potential conditions”). The properties of this potential allow us to extend the validity of a number of thermodynamic concepts well known for systems in or near thermal equilibrium to stationary states far from thermal equilibrium. The concept of symmetry breaking phase transitions for these systems is introduced in analogy to thermal equilibrium systems by considering the dependence of the stationary probability density of the system on a set of externally controlled parameters {λ}. A functional of the time dependent probability density of the system is defined in close analogy to the Gibb's definition of entropy. This functional has the properties of a Ljapunov functional of the governing Fokker-Planck equation showing the stability of the stationary probability density. The Langevin equations connected with the Fokker-Planck equation are considered. It is shown that, by means of the potential conditions, generalized “thermodynamic” fluxes and forces may be defined in such a way that the smoothly varying part of the Langevin equations (kinetic equations) constitutes a linear relation between fluxes and forces. The matrix of coefficients is given by the diffusion matrix of the Fokker-Planck equation. The symmetry relations which hold for this matrix due to the potential conditions then lead to the Onsager-Casimir symmetry relations extended to systems with detailed balance near stationary states far from thermal equilibrium. Finally it is shown that under certain additional assumptions the generalized thermodynamic potential may be used as a Ljapunov function of the kinetic equations.     

Brachistochrones in potential flow and the connection to Darwin's theorem

We establish the existence and the asymptotic properties of a path of minimum travel time for a line of particles starting upstream of a sphere or cylinder in potential flow. A connection is made between this brachistochrone path and Darwin's proposition which relates the added mass with the drift volume dragged by a body moving an infinite distance in the fluid. We compute an asymptotic correction to the drift volume for finite distances and show how the brachistochrone path is connected to the reflux volume. We present accurate numerical calculations for the brachistochrone position, point of zero horizontal Lagrangian displacement, reflux and partial drift volumes. These calculations are seen to agree well with the asymptotic predictions even for moderate values of the parameters. In the small Reynolds number regimes, we show that while for the case of Stokes flow past a sphere no brachistochrones exist at finite distances from the sphere, the Oseen correction is sufficient to restore such least-time trajectories. Lastly, the application to a sphere falling in a stratified fluid is discussed using the new drift volume correction formula.     

First-principles study of current–voltage characteristics of two-terminal carbon nanostructures

We present the first-principles investigation of the transport properties of nanotubes connected to metal electrodes under external bias potential. We have developed the technique to calculate the current–voltage (I–V) curves by using the local-density approximation in the density-functional theory. We apply this technique to Al-nanotube-Al systems with different contact geometries regarding the position, the orientation, and the distance of nanotube to the electrode. These different geometries at contact can play an important role in the transport properties. The I–V curves have the different behaviors although the nanotube is connected to the same electrode. The transmission rate from one electrode to the other electrode shows strong dependence on the contact geometry.     

Systematic trends in boron icosahedral structured materials

Boron materials exist in many different structures with an important similarity that they all contain connected B₁₂ icosahedra. Various structures that hold potential for super-hard material properties are examined using ab initio computational techniques. Systematic trends are established. The charge density between all B-B bonds in each structure that are examined and it is suggested that hardness of the material may, in part, relate to the average charge density between the boron bonds. Atoms connecting the B icosahedra donating charge that enhance the strength of the B-B bonds.     

Radiative-recombination transitions in sulphur-doped GaSb

Photoluminescence (PL) of sulphur-doped gallium antimonide prepared by a liquid-phase-electro-epitaxy growth method was investigated. Pumping-intensity-dependent and temperature-dependent PL measurements were carried out, properties of individual spectral bands were studied, and their physical origin was specified in detail. Sulphur caused compensation in GaSb, which is usually p-type if it is undoped due to the high concentration of its characteristic native acceptor (NA). As a result of compensation, recombination occurred under the condition of a fluctuating potential and spectral properties characteristic for such a material state were observed. Three bands formed the low-temperature PL spectra. Band A_U, connected with the NA, exhibited extremely low peak energy for some samples (down to 765 meV). Together with the presence of a “moving” PL, with a moving rate of approximately 10 meV per decade of the pumping intensity, it is a direct consequence of perturbed energy bands. Band S, peaking at about 732 meV, is a characteristic one for sulphur-doped GaSb and is most probably connected with a sulphur-donor-to-valence-band transition. The thermal decay of the band agrees with this supposition. Intensity-dependent and temperature-dependent PL of band A_I (maximum at 705-710 meV) both indicate that the band is connected with the ionised NA. PL intensity of the peak is relatively high, because compensation enhances the concentration of such centres.     

High field electrical properties of CdF2 crystals doped with rare earth ions

The electrical properties of CdF₂ crystals doped with Eu³⁺ and Gd³⁺ are described. A reversible “forming” effect is observed under high electric fields. The effect seems to be connected with a reversible modification of the potential barrier at the metal-insulator contact.     

Effective pair potentials in fluids in the presence of three-body forces

The physical properties of a fluid in which there is only a two-body potential, u_αβ , can be expressed in terms of the total correlation function, h ₁₂, which is a sum of all connected graphs with root-points on molecules 1 and 2, whose links are f bonds, where f_αβ = exp (-u_αβ/κT) - 1. It is shown that the total correlation function in the presence of a weak three-body potential, u_αβγ , is h ₁₂*, where h ₁₂* is the sum of all two-body connected graphs in which each f bond is replaced in turn by an f* bond, where

and where ? is a sub-set of the elementary graphs each of which contains one f_αβγ link. We call this sub-set the line-irreducible graphs, and its leading term is a graph discussed by Rushbrooke and Silbert.

The three-body potential is set equal to the dipole-dipole-dipole potential of Axilrod and Teller, and the analytic properties and numerical values of the first term ?₁ examined in detail.

Other effective potentials have been defined and the relations between them are elucidated. In particular it is shown that the first term in ? cannot be used to obtain the effective link f* at liquid densities, but that it can be compared with the dependence on density of the effective potential u* obtained by Mikolaj and Pings from the x-ray diffraction of compressed argon.     

Nonlinear transport through strongly correlated two-terminal heterostructures: a dynamical mean-field approach

The dynamical-mean-field method is applied to investigate the transport properties of heterostructures consisting of a strongly correlated electron system connected to metallic leads. The spectral function inside the correlated region is sensitive to the change of the interaction strength and bias voltage. Because of this sensitivity, current vs voltage characteristics of such heterostructures are rather nonlinear regardless of the detail of the potential profile inside the correlated region. The electronic properties such as the double occupancy are also changed by the bias voltage.     

Stationary frames in the Kerr field

Stationary frames in the Kerr geometry are rewieved and their properties compared. In particular, the locally non-rotating frame, the Carter frame, the static frame and the frame connected with the equatorial circular geodesic are treated as the most important examples.     

Conversion between kinetic energy and potential energy in the classical nonlocal Boltzmann equation

An important property of the classical Boltzmann equation is that kinetic energy is conserved. This is closely connected to the fact that the Boltzmann equation describes the nonequilibrium properties of an ideal gas. Generalizations of the Boltzmann equation to higher density involve, among other things, allowing the colliding particles to be at different positions. This spatial nonlocality is known to contribute to the density corrections of gas transport properties. For soft potentials such a spatial separation of the particles also leads to a conversion between kinetic and potential energy. In evaluating these effects the classical dynamics of the whole collision trajectory must be taken into account, involving also the time for the collision process. The resulting time nonlocality has usually been reinterpreted in terms of a spatial nonlocality. However, for a homogeneous system this is not possible and only the time nonlocality remains, this then being responsible for the conversion between kinetic and potential energy. This paper aims to clarify these properties of the nonlocal corrections to the classical mechanical Boltzmann collision term. Comments on the corresponding problem for the quantum Boltzmann equation are also made.