Two-dimensional Harmonic Potential Research Articles

APPLICATIONS OF CLASSICAL PERIODIC ORBIT THEORY TO CIRCULAR BILLIARDS WITH SMALL SCATTERING CENTERS

Mesoscopic systems like metallic clusters in three dimensions as well as quantum dots in two dimensions have raised a particular interest in the semiclassical interpretation of shell effects. We use periodic orbit theory to calculate the density of states for two-dimensional circular billiards. When a singular magnetic flux line is added at the center of the disk, we show that the Aharonov-Bohm (AB) effect manifests itself through the cancellation of periodic orbits and the appearance of a new signal in the Fourier transform of the quantum density of states. The same effects are also found analytically for a two-dimensional harmonic oscillator potential with flux line. Finally, we show that a homogeneous magnetic field B perpendicular to the disk plane leads to B-periodic oscillations of the level density, which recently have also been observed experimentally in two-dimensional circular quantum dots.

The steady-state Green's function method in unimolecular reactions. Generalization of the MFPT concept. I. Irreversible reactions

Abstract We investigate two forms of macroscopic kinetic equations for evaluation of different reaction rate constants for irreversible unimolecular reactions in liquids. The steady-state differential and integral equations for calculation of the rate constants were formulated. New forms of the Green's function, the steady-state Green's functions, convenient for calculation of the rate constant, were introduced and their physical meaning was established. The concept of the mean first passage time (MFPT) was generalized from the “MFPT to a point” to the definition of the “effective MFPT”. The effective MFPT was defined as the average time for particles to reach a region on the surface, rather than a point. Applications of the steady-state Green's function method as well as the effective MFPT concept are shown for one- and two-dimensional potential surface reactions. The rate constant for the one- and two-dimensional harmonic oscillator and bistable potentials are presented for all barrier heights.

Dynamical parasuperalgebras of parasupersymmetric harmonic oscillator, cyclotron motion and Morse Hamiltonians

Simple quantum mechanical systems that have natural generalisations of superalgebras as dynamical algebras are discussed. The authors propose to call these new algebras parasuperalgebras. The symmetry generators of 'spin-1' particles in one-dimensional harmonic potentials are shown to realise an algebra endowed with a symmetric trilinear product. Spin-1 particles in constant magnetic fields or in two-dimensional harmonic potentials have analogous constants of motion that are described. It is also indicated how these conserved charges provide a spectrum-generating algebra for the parasupersymmetric generalisation of the Morse Hamiltonian. These concrete models should be useful in identifying the abstract properties of parasuperalgebras.

A Closed Form Green Function Describing Diffusion in a Strained flow Field

Stationary concentration profiles resulting from the two-dimensional diffusion of material away from a continuous source in an advective flow field on the infinite plane are considered. The advection field contains a straining component, in addition to a spatially uniform part. The inhomogeneous advection-diffusion equation describing the spreading away from the source can be transformed to a noncentrally forced Schrodinger equation with a two-dimensional harmonic oscillator potential. The exact solution of this equation is given in terms of a definite integral, being an incomplete integral representation of thezeroth order modified Bessel function of the second kind (to which it reduces in appropriate circumstances). The field dependence is present not only in the kernel function, but also in one of the limits of integration. The near-field limit leads to concentration profiles in which curvature effects of the straining flow field may be neglected in comparison to the uniformly advecting part. Taking th...

Non-periodic local motion of silver ions in ßAg 3SI from far-infrared conductivity measurements

The frequency dependent far-infrared conductivity of ßAg 3SI, determined by measurement of transmittance and reflectivity, provides dynamic evidence for a non-periodic local motion of the silver ions. This motion takes place in the areas at the centers of the iodine-cube faces where the cationic potential is known to be flat. The experimental far-infrared conductivity is compared with conductivity spectra calculated on the basis of the following simple single-particle models: diffusion on a ring, statistical hopping between nearest-neighbor tetrahedral sites, and Brownian motion in a two-dimensional harmonic potential.

Pairing and quadrupole forces in a two-dimensional soluble model

The model treated is a system of particles moving in a two-dimensional harmonic oscillator potential with two-body pairing and quadrupole forces mixing states within a single major shell. A simple representation is found in which the Hamiltonian is exactly diagonal. An “energy gap” is obtained in the limit of pure pairing forces and rotational spectra in the limit of pure quadrupole forces. In the intermediate region the spectrum varies from energy gap to rotational as the number of particles is increased. The effective moment of inertia of the rotational band is unaffected by the pairing force, remaining constant at the value for a pure quadrupole force. The model is also treated by replacing the quadrupole force by a self-consistent deformed field and the moment of inertia is calculated using the cranking model. The results agree with the exact solution. Implications of the model for more realistic cases are discussed.