Constant Electrostatic Potential Research Articles

Donor binding energies in a spherical core–shell quantum dot: parabolic and shifted parabolic shell potentials

The effects of parabolic and shifted parabolic potentials on centred hydrogenic impurity-related binding energies are studied. This is theoretically achieved by solving the Schrodinger equation within the effective mass approximation. The hydrogenic impurity situates in the core of a spatially constant electrostatic potential, surrounded by a shell material which has either an intrinsic parabolic potential or shifted parabolic potential. For a given outer radius of the shell, the parabolic potential enhances binding energies (with greater enhancement for small radii of the core), while the shifted parabolic potential dwindles binding energies for small cores, and increases the binding energies for larger cores. An increase in the spatially invariant potential in the core results in reduced binding energies, with appreciable decrement occurring in core–shell structures that have wider cores.

Instability of a Charged Droplet in an Inhomogeneous Electrostatic Field of a Rod of Finite Thickness

The instability of a charged droplet of an ideal liquid in an inhomogeneous electrostatic field of a rod of finite thickness maintained at a constant electrostatic potential is investigated within the framework of analytic asymptotic calculations. It is shown that the mode amplitudes and the drop oscillation frequencies increase with the rod thickness. The critical conditions of instability of the droplet reduce by several times as compared with the critical conditions of implementation of its instability in the electrostatic field of an infinitely thin filament maintained at a constant electrostatic potential. An analytic dependence between the charge and field parameters, critical for implementation of the instability of a charged droplet in an inhomogeneous electrostatic field and dependent on the rod thickness, is found.

Collisionless damping of geodesic acoustic mode in plasma with nonextensive distribution

Geodesic acoustic mode (GAM) in collisionless toroidal plasmas with a constant electrostatic potential around a magnetic surface is investigated based on the linear gyrokinetic theory in context of nonextensive statistics mechanics. The damping rate of GAM is shown to be dependent on the nonextensive parameters of ions, and in the extensive limit, the result in Maxwellian distribution plasma is recovered. The damping rate is found to be enhanced as the nonextensive parameter of ion decreases.

Localization of the phantom force induced by the tunneling current

The phantom force is an apparently repulsive force, which can dominate the atomic contrast of an AFM image when a tunneling current is present. We described this effect with a simple resistive model, in which the tunneling current causes a voltage drop at the sample area underneath the probe tip. Because tunneling is a highly local process, the areal current density is quite high, which leads to an appreciable local voltage drop that in turn changes the electrostatic attraction between tip and sample. However, Si(111)-7$\ifmmode\times\else\texttimes\fi{}$7 has a metallic surface state and it might be proposed that electrons should instead propagate along the surface state, as through a thin metal film on a semiconducting surface, before propagating into the bulk. In this paper, we first measure the phantom force on a sample that displays a metallic surface state [here, Si(111)-7$\ifmmode\times\else\texttimes\fi{}$7] using tips with various radii. If the metallic surface state would lead to a constant electrostatic potential on the surface, we would expect a direct dependence of the phantom force with tip radius. In a second set of experiments, we study H/Si(100), a surface that does not have a metallic surface state. We conclude that a metallic surface state does not suppress the phantom force, but that the local resistance ${R}_{s}$ has a strong effect on the magnitude of the phantom force.

Rodrigues solution of the Dirac equation for fields obtained from the master function formalism

We show that the radial Dirac equation with constant electrostatic potential and for a large class of the field potentials which are obtained from the master function formalism can be solved by the Rodrigues representation of the orthogonal polynomials. We also show that the Schrödinger-like differential equation obtained from the Dirac equation satisfies the supersymmetry and shape invariant conditions in non-relativistic quantum mechanics. The relativistic energy spectrum for a given potential function is calculated from its corresponding non-relativistic energy spectrum.

NeMo: A network model program for analyzing the thermoelectric properties of meso and nanostructured composite materials

We present our NeMo program package where we implemented a network model for calculating the thermoelectric properties, i.e. total electric and thermal reiststances and total Seebeck coefficient, of structured composite materials. The real structure of the composite sample is translated into a pixel grid where local transport properties are assigned to each pixel including bulk-like properties as well as interface properties to adjacent pixels which can be adjusted to account for real interfaces. The resulting networks are embedded between a left and a right contact, each at constant temperature and constant electrostatic potential. By using nodal analysis, the total thermal and electric resistances of the structure, as well as local voltages or temperature differences between the pixels are obtained. In an additional step, the local temperature differences are used to simulate local Seebeck voltages as voltage sources between the pixels in order to obtain the total Seebeck voltage and, thus, the Seebeck coefficient, of the structure. In a series of examples, we discuss the merits and limitations of the model for describing the thermoelectric properties of various composite materials of interest and demonstrate that, despite its simplicity, it may yield helpful insight into the correlation between mesoscopic structure and macroscopic thermoelectric properties.

Multiple eigenmodes of geodesic acoustic mode in collisionless plasmas

We report a series of eigenmodes of the geodesic acoustic mode (GAM), which includes the standard GAM, a branch of low-frequency mode, and a series of ion sound wave-like modes. The case of Ti≫Te is investigated, and eigenfrequencies of these modes are obtained analytically from a linear gyrokinetic model in collisionless plasmas with a rigid constant electrostatic potential around a magnetic surface.

On the influence of the water electrostatic field on the amide group vibrational frequencies.

For clusters of N-methylacetamide and water molecules the performance of the fixed-charged approximation was tested against continuum and explicit ab initio models. The dispersion of the vibrational frequencies when constant electrostatic potential was maintained at the solute atoms was compared to the distribution caused by geometry fluctuations.

Charge distribution and stability of charged carbon nanotubes.

Density-functional calculations of charge distribution on negatively and positively charged nanotubes result in charge density profiles characterized by a significant increase of charge density at the tube ends. These results are in quantitative agreement with classical electrostatic analysis, which assumes constant electrostatic potential on the conductive tube surface. At high charging levels, the tube ends are observed to be unstable due to Coulomb repulsion. By combining ab initio calculations with classical electrostatics, we determine, as a function of tube length and geometry of the tube end, the critical voltage beyond which nanotubes are unstable.

Thermodynamics of(3+1)-dimensional black holes with toroidal or higher genus horizons

We examine counterparts of the Reissner-Nordstrom-anti-de Sitter black hole spacetimes in which the two-sphere has been replaced by a surface Sigma of constant negative or zero curvature. When horizons exist, the spacetimes are black holes with an asymptotically locally anti-de Sitter infinity, but the infinity topology differs from that in the asymptotically Minkowski case, and the horizon topology is not S^2. Maximal analytic extensions of the solutions are given. The local Hawking temperature is found. When Sigma is closed, we derive the first law of thermodynamics using a Brown-York type quasilocal energy at a finite boundary, and we identify the entropy as one quarter of the horizon area, independent of the horizon topology. The heat capacities with constant charge and constant electrostatic potential are shown to be positive definite. With the boundary pushed to infinity, we consider thermodynamical ensembles that fix the renormalized temperature and either the charge or the electrostatic potential at infinity. Both ensembles turn out to be thermodynamically stable, and dominated by a unique classical solution.

The effect of an electrostatic field on inviscid liquid flow down an inclined plane

For a study of nonlinear wave motion under an electrostatic field, the Korteweg-de Vries (KdV) equation for inviscid liquid film flowing under gravity down an inclined plane has been derived, and the effect of the electric field on the stability of a solitary wave as a solution of the KdV equation is examined. Under a constant electrostatic potential the stability of the wave is not affected. However, with a slowly varying potential it becomes unstable.

Gyrofluid turbulence models with kinetic effects

Nonlinear gyrofluid equations are derived by taking moments of the nonlinear, electrostatic gyrokinetic equation. The principal model presented includes evolution equations for the guiding center n, u∥, T∥, and T⊥ along with an equation expressing the quasineutrality constraint. Additional evolution equations for higher moments are derived that may be used if greater accuracy is desired. The moment hierarchy is closed with a Landau damping model [G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64, 3019 (1990)], which is equivalent to a multipole approximation to the plasma dispersion function, extended to include finite Larmor radius effects (FLR). In particular, new dissipative, nonlinear terms are found that model the perpendicular phase mixing of the distribution function along contours of constant electrostatic potential. These ‘‘FLR phase-mixing’’ terms introduce a hyperviscositylike damping ∝k⊥2‖Φkk×k′‖, which should provide a physics-based damping mechanism at high k⊥ρ which is potentially as important as the usual polarization drift nonlinearity. The moments are taken in guiding center space to pick up the correct nonlinear FLR terms and the gyroaveraging of the shear. The equations are solved with a nonlinear, three-dimensional initial value code. Linear results are presented, showing excellent agreement with linear gyrokinetic theory.

Atomistic simulation of oxide surfaces

This paper is concerned with the atomistic simulation of the surfaces of MgO, CaO, SrO, Li2O, c-ZrO2, SrTiO3, α-Al2O3 and α-Fe2O3. Details are reported of the structure and energy of pure, non-defective surfaces and the constant electrostatic potential in the bulk that results from surface relaxation and electronic polarisation. Cation impurity segregation is discussed in some detail with an emphasis on calculated heats of segregation, equilibrium surface coverages, the lattice structure of segregated surfaces and the energy of impure surfaces.

Quantum percolation and quantization of Hall resistance in two-dimensional electron gas

A theory of the quantized Hall resistance ${R}_{\mathrm{xy}}$ in a two-dimensional electron gas is presented. The exactness of the quantization is explained as a purely topological effect. It is shown that lines of constant electrostatic potential represent an effective wave guide for electron waves. In the Corbino ring geometry the condition for quantization of ${R}_{\mathrm{xy}}$ is the existence of equipotentials encircling the central electrode. The quantum of ${R}_{\mathrm{xy}}=\frac{h}{{e}^{2}}$ is shown to be unaffected by a random scattering potential. Collapse of the Hall current on increasing disorder is interpreted as a percolation transition.

Enhanced probability for the photoelectric effect in a Faraday cage

AbstractThe cross section for the photoelectric effect is calculated for the case where the photoionization takes place within a Faraday cage held at a constant electrostatic potential. When the geometry has spherical symmetry, and when the potential is repulsive, the cross section is enhanced by a factor E/(E − V0). The predicted effect is a purely quantum mechanical one, since according to classical electrodynamics, no forces due to the potential of the cage will act on a charged particle in the fieldfree region inside it. In quantum theory, the effect arises because the continuum states extend to the region outside the cage.

Two-dimensional plasma equilibrium in a magnetic field

A criterion for two-dimensional plasma equilibrium is derived from the Vlasov equation. It may be shown that particle densities are constant on any surface of constant electrostatic potential only if the plasma drift kinetic energies are constant on the electrostatic equipotential surfaces.

Two-Dimensional, Time-Independent Solutions for Plasma Moving through a Uniform Transverse Magnetic Field

If particle gyroradii and drift velocities are small in a collisionless plasma which is infinite and uniform in the direction of the straight magnetic field B, it may be shown in the time-independent case that particle densities and B are constant on any surface of constant electrostatic potential. Using the magnetohydrodynamic equation of motion, it follows that the particles move very nearly along these equipotential surfaces, and an expression for the charge density may be derived. From the resulting Poisson equation, solutions for plasma crossing a uniform B0 field may be obtained; collectively these solutions may appropriately be termed the ``double-vortex'' model from their drift velocity patterns.

Acoustic diffraction by an annular disc

The problem of diffraction of a general acoustic wave by a soft annular disc is discussed. This three part boundary-value problem is reduced to a set of integral equations, which can be solved by an iterative process when the frequency of the incident wave is low and the inner radius of the annular disc is small. A special study is made of a particular case. When the incident wave is an axisymmetric plane wave the problem is governed by a set of four integral equations. The iterative solutions of these four integral equations are found and an approximate value of the plane wave scattering cross-section for a soft annular disc is calculated. These results are used to determine two well-known expressions, namely, the plane wave scattering cross-section for a soft disc and the capacity of an annular disc held at a constant electrostatic potential.