Current partition in multiprobe conductors in the presence of slowly oscillating external potentials

In the presence of a static potential drop a carrier stream incident at a contact of the sample is partitioned into the other contacts according to the transmission probabilities of the sample. The bare response to oscillating potentials, on the other hand, violates current conservation due to the piling up of unscreened charges in the sample, and has to be modified by taking the induced screening potential into account. We present a novel derivation of the conductance response to oscillating external chemical potentials, find the response to an arbitrary internal potential in terms of functional derivatives with respect to the local potential of the scattering matrix of the conductor, and determine the screening potential for slowly oscillating potentials from the condition of local charge neutrality. We find that the current partitioning depends on ratios of local densities of states which reflect the injection and emission properties of the contacts of the sample.     

Scattering of massless Dirac particles by oscillating barriers in one dimension

We study the scattering of massless Dirac particles by oscillating barriers in one dimension. Using the Floquet theory, we find the exact scattering amplitudes for time-harmonic barriers of arbitrary shape. In all cases the scattering amplitudes are found to be independent of the energy of the incoming particle and the transmission coefficient is unity. This is a manifestation of the Klein tunneling in time-harmonic potentials. Remarkably, the transmission amplitudes for arbitrary sharply-peaked potentials also become independent of the driving frequency. Conditions for which barriers of finite width can be replaced by sharply-peaked potentials are discussed.     

The electromagnetic field in finite crystals

The electromagnetic potentials of a finite crystalline slab of oscillating point charges are separated into parts with distinct properties. One part is the Ewald potential.     

Static potential renormalization in time-dependent fields

We consider the scattering of electrons at a static potential under the influence of an additional time-dependent, homogeneous electric field (‘microwave’). Starting from a plane wave basis, we derive a generalization of the Born (first) order approximation in arbitrary strong oscillating fields. As an example, we evaluate the Friedel density oscillations around a static scatterer whose potential is renormalized by the microwave. The microwave leads to a band of inelastic scattering channels with effective potentials, the shape of which can be ‘tuned’ by the microwave polarization and strength.     

Solution of the Hartree-Fock equations

We suggest to use the Newton iteration method for constructing a (locally unique) solution of the atomic and nuclear Hartree-Fock equations for an arbitrary number of particles. Our proposal is based on a theorem by Kantorovi and rests on the following points: 1) the two-body potential must satisfy a boundedness condition; 2) the zero-order approximation, used to start the iteration sequence, must satisfy certain conditions, to be proved numerically. Condition 1) holds, for instance, for all local potentials, defined by a bounded function and for a class of nonlocal potentials; it does not hold for local potentials, behaving as 1/r near the origin.This work has been supported in part by Istituto Nazionale di Fisica Nucleare (Sezione di Catania) and by Centro Siciliano di Fisica Nucleare e di Struttura della Materia (Catania).     

On the generalization of the Enskog equation to the case of steep repulsive potentials

For a classical homogeneous system of particles interacting via steeply repulsive potentials a generalization of the Enskog equation is proposed. This kinetic equation has the properties that it reduces to the usual Enskog equation in the limit of hard-sphere potentials and that the total instead of the kinetic energy is conserved in the system. The expression for the potential energy obtained is correct at arbitrary densities in equilibrium.     

Densities of electron’s continuum in gravitational and electromagnetic fields

Relativistic dynamics of distributed mass and charge densities of the extended classical particle is considered for arbitrary gravitational and electromagnetic fields. Both geodesic and field gravitational equations can be derived by variation of the same Lagrange density in the classical action of a nonlocal particle distributed over its radial field. Vector geodesic relations for material space densities are contraction consequences of tensor gravitational equations for continuous sources and their fields. Classical four-flows of elementary material space depend on local electromagnetic fourpotentials for charged densities, as in quantum theory. Besides the Lorentz force, these potentials result in two more accelerating factors vanishing under equilibrium internal stresses within the continuous particle.     

Particle densities for dilute hard-sphere Bose or Fermi gases in an external potential

We prove that if the diameter of a hard-sphere is much smaller than the size of an external potential, the s-wave pseudopotential reduces to the Huang-Yang s-wave pseudopotential. We obtain the first-order virial expansions of particle densities for dilute hard-sphere Bose or Fermi gases in an arbitrary external potential. In the absence of an external potential, the results reduce to the Huang-Yang-Luttinger and Lee-Yang virial expansions. In the quasi-classical limit, the results reduce to the results of the local density approximation.     

The Poisson-Helmholtz-Boltzmann model

We present a mean-field model of a one-component electrolyte solution where the mobile ions interact not only via Coulomb interactions but also through a repulsive non-electrostatic Yukawa potential. Our choice of the Yukawa potential represents a simple model for solvent-mediated interactions between ions. We employ a local formulation of the mean-field free energy through the use of two auxiliary potentials, an electrostatic and a non-electrostatic potential. Functional minimization of the mean-field free energy leads to two coupled local differential equations, the Poisson-Boltzmann equation and the Helmholtz-Boltzmann equation. Their boundary conditions account for the sources of both the electrostatic and non-electrostatic interactions on the surface of all macroions that reside in the solution. We analyze a specific example, two like-charged planar surfaces with their mobile counterions forming the electrolyte solution. For this system we calculate the pressure between the two surfaces, and we analyze its dependence on the strength of the Yukawa potential and on the non-electrostatic interactions of the mobile ions with the planar macroion surfaces. In addition, we demonstrate that our mean-field model is consistent with the contact theorem, and we outline its generalization to arbitrary interaction potentials through the use of a Laplace transformation.     

Scalar-tensor cosmologies with a potential in the general relativity limit: Time evolution

We consider Friedmann–Lemaître–Robertson–Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling function and potential. For the era when the cosmological energy density of the scalar potential dominates over the energy density of ordinary matter, we use a nonlinear approximation of the decoupled scalar field equation for the regime close to the so-called limit of general relativity where the local weak field constraints are satisfied. We give the solutions in cosmological time with a particular attention to the classes of models asymptotically approaching general relativity. The latter can be subsumed under two types: (i) exponential convergence, and (ii) damped oscillations around general relativity. As an illustration we present an example of oscillating dark energy.     

The Universality Classes in the Parabolic Anderson Model

We discuss the long time behaviour of the parabolic Anderson model, the Cauchy problem for the heat equation with random potential on $\mathbb{Z}^{d}We discuss the long time behaviour of the parabolic Anderson model, the Cauchy problem for the heat equation with random potential on. We consider general i.i.d. potentials and show that exactly four qualitatively different types of intermittent behaviour can occur. These four universality classes depend on the upper tail of the potential distribution: (1) tails at ∞ that are thicker than the double-exponential tails, (2) double-exponential tails at ∞ studied by G?rtner and Molchanov, (3) a new class called almost bounded potentials, and (4) potentials bounded from above studied by Biskup and K?nig. The new class (3), which contains both unbounded and bounded potentials, is studied in both the annealed and the quenched setting. We show that intermittency occurs on unboundedly increasing islands whose diameter is slowly varying in time. The characteristic variational formulas describing the optimal profiles of the potential and of the solution are solved explicitly by parabolas, respectively, Gaussian densities. Our analysis of class (3) relies on two large deviation results for the local times of continuous-time simple random walk. One of these results is proved by Brydges and the first two authors in [BHK04], and is also used here to correct a proof in [BK01].     

Big islands in dispersing billiard-like potentials

We derive a rigorous estimate of the size of islands (in both phase space and parameter space) appearing in smooth Hamiltonian approximations of scattering billiards. The derivation includes the construction of a local return map near singular periodic orbits for an arbitrary scattering billiard and for the general smooth billiard potentials. Thus, universality classes for the local behavior are found. Moreover, for all scattering geometries and for many types of natural potentials which limit to the billiard flow as a parameter ε→0, islands of polynomial size in ε appear. This suggests that the loss of ergodicity via the introduction of the physically relevant effect of smoothening of the potential in modeling, for example, scattering molecules, may be of physically noticeable effect.     

Cosmological evolution in compactified Horava-Witten theory induced by matter on the branes

The combined Einstein equations and scalar equation of motion in the Horava-Witten scenario of the strongly coupled heterotic string compactified on a Calabi-Yau manifold are solved in the presence of additional matter densities on the branes. We take into account the universal Calabi-Yau modulus with potentials in the 5-d bulk and on the 3-branes, and allow for an arbitrary coupling of the additional matter to and an arbitrary equation of state. No ad hoc stabilization of the five dimensional radius is assumed. The matter densities are assumed to be small compared to the potential for on the branes; in this approximation we find solutions in the bulk which are exact in y and t. Depending on the coupling of the matter to and its equation of state, various solutions for the metric on the branes and in the 5-d bulk are obtained: solutions corresponding to a ”rolling radius”, and solutions with a static 5-d radius, which reproduce the standard cosmological evolution. Received: 8 April 2002 / Published online: 26 July 2002     

Regularity of Local Minimizers of the Interaction Energy Via Obstacle Problems

The repulsion strength at the origin for repulsive/attractive potentials determines the regularity of local minimizers of the interaction energy. In this paper, we show that if this repulsion is like Newtonian or more singular than Newtonian (but still locally integrable), then the local minimizers must be locally bounded densities (and even continuous for more singular than Newtonian repulsion). We prove this (and some other regularity results) by first showing that the potential function associated to a local minimizer solves an obstacle problem and then by using classical regularity results for such problems.     

Equivalent local potentials for a coupled-channel system and the Feshbach optical potential

Explicit formulas of all equivalent local potentials for a coupledn-channel problem are calculated. The general equivalent local potentials constitute a -complex-parameter family of local potentials. For a definite input elastic channel, the uniqueness of the equivalent local potential is shown. The equivalent local potential of the Feshbach optical potential coincides with the equivalent local potential of then-channel system. The construction of the Feshbach optical potential is a reduction to the dimensionality of the coupled-channel problem, the construction of the equivalent local potential is a diagonalization of the coupled-channel problem, both constructions are compatible manipulations on the set of the coupled-channel system. The properties of the Feshbach optical potential can be used for the study of the properties of the equivalent local potential.     

Confinement and deconfinement in the potential of antidot arrays of a massless Dirac electron in magnetic fields

We have investigated the effect of inter-Landau level mixing on confinement/deconfinement in antidot potentials of states with energies less than the potential height of the antidot array. We find that, depending on the ratio between the size of the antidot R and the magnetic length [Formula: see text], probability densities display confinement or deconfinement in antidot potentials (B is the magnetic field). When R/???1 form a nearly degenerate band and their probability densities are independent of k, in contrast to the case of R/??相似文献   

Time-dependent density-functional theory beyond the local-density approximation

Approximations for the ground-state exchange-correlation potential of density-functional theory have reached a high level of sophistication. By contrast, time- or frequency-dependent exchange-correlation potentials are still being treated in a local approximation. Here we propose a novel approximation scheme, which effectively brings the power of the generalized gradient approximation (GGA) and meta-GGA to time-dependent density-functional theory. The theory should allow a more accurate treatment of strongly inhomogeneous electronic systems (e.g. molecular junctions) while remaining essentially exact for slowly varying densities and slowly varying external potentials.     

Correlation Estimates in the Anderson Model

We give a new proof of correlation estimates for arbitrary moments of the resolvent of random Schrödinger operators on the lattice that generalizes and extends the correlation estimate of Minami for the second moment. We apply this moment bound to obtain a new n-level Wegner-type estimate that measures eigenvalue correlations through an upper bound on the probability that a local Hamiltonian has at least n eigenvalues in a given energy interval. Another consequence of the correlation estimates is that the results on the Poisson statistics of energy level spacing and the simplicity of the eigenvalues in the strong localization regime hold for a wide class of translation-invariant, selfadjoint, lattice operators with decaying off-diagonal terms and random potentials.     

Pair correlation functions for exchange and correlation in uniform spin densities

The correlation holes for densities of equal and opposite spin around a test electron are determined from the Schrödinger equation with proper boundary conditions. The traditional `exchange' term follows from the boundary condition which respects a spacial exclusion principle for equal spins. The resulting potential compares reasonably well with standard local density potentials and the approach is feasible for extensions towards non-local effects.