Two-dimensional reaction-diffusion equations with simple reaction kinetics are used to study the dynamics of spiral waves in excitable media. Detailed numerical results are presented for the transition from simple (periodic) rotation to compound (quasiperiodic) rotation of spiral waves. It is shown that this transition occurs via a supercritical Hopf bifurcation and that there is no frequency locking within the quasiperiodic regime.

The propagation of an ultrashort ionizing electromagnetic pulse in a uniform plasma is investigated. It is shown that together with frequency up-conversion there is a strong compression of the pulse. This phenomenon occurs due to an alternative mechanism involving self-steepening and field collapse with wave energy trapping into a singularity.

It is shown that n>0 simple-harmonic-oscillator squeezed states have the same time-evolution behavior as the fundamental (n=0) squeezed state. That is, the probability density ‖ψ(x,t)${\mathrm{\Vert }}^2$ retains its original shape as time progresses, except that the scales of the ordinate and abscissa oscillate in a reciprocal manner with frequency 2ω. This allows the time-evolved squeezing operator S${\mathrm{^}}_{\mathit{H}}$(λ,t) to be written as a product of simple factors. Moreover, if a thermal distribution with density matrix ρ^ is squeezed, then the mixed squeezed state with minimum free energy has a density matrix given by a unitary transformation ρ${\mathrm{^}}_{\mathit{s}}$=S^(λ)ρ^S^ ${}_{}{}^{\mathrm{°}}{}_{}{}^{}$(λ), where λ is a suitable squeezing parameter.

An algorithm previously obtained for complex-energy modal probabilities in non-Hermitian quantum dynamics is generalized to determine expectation values for arbitrary observables. When cast in conventional form, the formalism including the generalized algorithms appears as a natural generalization of conventional quantum theory, in that conventional quantum theory obtains in the continuous Hermitian limit.

We present a theoretical analysis of transient diffractions in nematic liquid crystals, where the nonlinear optical response is due to laser-induced changes in the temperature, density, and director axis reorientation. Our solutions of the field-induced reorientation equation and the coupled density and thermal conduction equations provide a quantitative theoretical model for the experimentally observed grating diffractions, oscillations, and relaxation phenomena.

This paper investigates the stability of intense optical slab beams in infinite plasmas. Profiles depending on the distance x were found in a recent paper by Kurki-Suonio, Morrison, and Tajima [Phys. Rev. A 40, 3230 (1989)]. The most useful profiles were in the form of solitons. Solutions for which the beam profile was of oscillatory character were also found. Here a stability analysis is performed on all these profiles. The results, in terms of the physical cylindrical variables, imply radial stability but azimuthal instability of the solitons. The wave structures, however, are also unstable in the radial direction, and this explains numerical results of Kurki-Suonio et al.

We extend a previous analysis of the propagation of energy packets in a one-dimensional model for the DNA double helix by studying how various types of inhomogeneities in the molecule affect the transfer of solitonlike energy packets along the chain.

We investigate the predictions of random-matrix theory for the eigenvector statistics and compare them with eigenmodes of kicked tops under conditions of classical chaos. The well-known ${\mathrm{\chi }}_{\nu }^2$ distribution finds an interesting application with ν=1, 2, and 4 for the orthogonal, unitary, and symplectic universality class, respectively. The change of the eigenvector statistics accompanying the classical transition from chaotic to regular motion is also considered.

Simple experiments demonstrate the importance of particle irregularity on the flow of granular materials. We introduce cellular automata to model these flows with rules that are derived from experiments. Automata that model nonspherical particles can reproduce a number of important features of the physical flows, including alignment of the particles, the formation of a complex channel region, the formation of defects in the body of the material, and the overall shape of the upper free surface of the material.

It is shown that, for a given tokamak cross-sectional shape and arbitrary values of the magnetic axis safety factor ${\mathit{q}}_0$, the first stability condition against pressure-driven magnetohydrodynamic modes has the form 40πβ${\mathit{aB}}_0$/I≤${\mathit{C}}_{\mathit{R}}$(${\mathit{q}}_0$)/${\mathit{q}}_0$. Moreover, in the limit of large ${\mathit{q}}_0$, ${\mathit{C}}_{\mathit{R}}$(${\mathit{q}}_0$) becomes independent of ${\mathit{q}}_0$ and independent of the toroidal mode number.

The difficulties associated with application of the shifted large-N technique to the Dirac equation have been resolved by applying the method to the Klein-Gordon equation in which a spin-orbit interaction term is included analogous to Pauli theory. Explicit analytical expressions for the relativistic screened Coulomb bound-state energies, radial wave functions, and normalizations are given. For the point-Coulomb problem, we restore exact results for the relativistic binding energies and almost exact wave functions. The 1/N expansion results are then compared with the exact numerical solutions as well as with those obtained in other analytical methods for a number of screened Coulomb potentials and for a wide range of atomic numbers Z. In general, excellent agreement is found. In contrast to the limited applicability of the usual perturbative methods, our technique is found to be flexible and may be extended to a more general class of relativistic potentials that has applications in atomic and quarkonium physics. Encouraging aspects of the present approach are also briefly discussed.

The relativistic shift, including the corrections to the binding energy due to vacuum polarization, the hyperfine splitting, and nuclear finite-size effects have been calculated for the (J=1,ν=1) states of ddμ and dtμ. The corrections have been determined by first-order perturbation theory using the nonrelativistic wave functions determined by Alexander and Monkhorst [S. A. Alexander and H. J. Monkhorst, Phys. Rev. A 38, 26 (1988)]. The results show rapid convergence with basis-set size. The overall convergence of the calculations is better than 0.01 meV. The accuracy of the total correction to the binding energies is estimated to be ±0.5 meV.

We consider a particle in a three-dimensional potential V(r) or in a one-dimensional potential V(x). We use a Green’s-function approach to show that for many V’s of interest one can obtain a necessary condition for the existence of a bound state below a specified energy that is somewhat stronger than the usual condition; furthermore, results can be obtained for V(r)≠V(r), under some special restrictions, which utilize an integral containing only one, not two, Green’s functions.

We consider a positive diatomic molecule consisting of N electrons and two nuclei and obtain some results that exhibit scaling properties of the adiabatic energy ${\mathit{E}}_{\mathrm{ad}}$—the ground-state energy with the nuclei fixed—under changes in the charges, and we obtain lower bounds on ${\mathit{E}}_{\mathrm{ad}}$. In particular, with the use of available numerical results for ${\mathit{E}}_{\mathrm{ad}}$ for a single electron in the Coulomb field of two fixed nuclei with charges ${\mathit{Z}}_{\mathit{A}}$e and ${\mathit{Z}}_{\mathit{B}}$e, we show that composite bound states cannot be formed for N=1 and ${\mathit{Z}}_{\mathit{A}}$+${\mathit{Z}}_{\mathit{B}}$≥3 nor for N=2 and ${\mathit{Z}}_{\mathit{A}}$=${\mathit{Z}}_{\mathit{B}}$≥3, results not too far from the true lower limits.

We investigate the convergence of Mo?ller-Plesset–Goldstone perturbation-theory expansions around the g-Hartree, Hartree-Fock, and scaled Hartree-Fock mean fields for quantum-chemical models of the beryllium atom and the lithium hydride molecule. We use a finite Hilbert space of many-electron functions constructed from a finite Gaussian basis set of atomic orbitals. In this space it is possible to diagonalize the nonrelativistic Hamiltonian exactly and to calculate perturbation expansions in high order. Our results show significantly faster convergence for perturbation expansions around the g-Hartree mean fields in a large range of the mean-field parameter.

A systematic procedure to construct approximants to the solution of the Thomas-Fermi equation for isolated neutral atoms is presented. The method takes into account the power-series expansions of the solution of the Thomas-Fermi equation for small and large values of the coordinate and matches them. The initial slope is accurately calculated and the approximants are shown to represent the solution for all values of the coordinate with reasonable accuracy. The method is presented in a general way so that it can be applied to other problems of physical interest.

For the purpose of improving upon present approximate functionals, nonuniform coordinate scaling is introduced into density-functional theory, where ${\mathit{n}}_{\lambda }^{\mathit{x}}$(x,y,z)=λn(λx,y,z) is an example of a nonuniformly scaled electron density. Inequalities are derived for the exact noninteracting kinetic energy ${\mathit{T}}_{\mathit{s}}$[n]. For example, ${\mathit{T}}_{\mathit{s}}$[${\mathit{n}}_{\lambda }^{\mathit{x}}$]≤${\lambda }^2$${\mathit{T}}_{\mathit{s}}^{\mathit{x}}$[n]+${\mathit{T}}_{\mathit{s}}^{\mathit{y}}$[n]+${\mathit{T}}_{\mathit{s}}$ ${}_{}{}^{\mathit{z}}{}_{}{}^{}]$, where ${\mathit{T}}_{\mathit{s}}^{\mathit{x}}$,${\mathit{T}}_{\mathit{s}}^{\mathit{y}}$, and ${\mathit{T}}_{\mathit{s}}^{\mathit{z}}$ are the x,y, and z components of ${\mathit{T}}_{\mathit{s}}$. Surprisingly, the gradient expansion through fourth order violates the inequalities. We also observe that the Thomas-Fermi approximation for ${\mathit{T}}_{\mathit{s}}$,${\mathit{T}}_{\mathit{s}}^{\mathrm{TF}}$, and the local-density approximation for the exchange-correlation energy, ${\mathit{E}}_{\mathrm{xc}}^{\mathrm{LDA}}$, do not distinguish between nonuniform scaling along different coordinates. That is, ${\mathit{T}}_{\mathit{s}}^{\mathrm{TF}}$[${\mathit{n}}_{\lambda }^{\mathit{x}}$]=${\mathit{T}}_{\mathit{s}}^{\mathrm{TF}}$[${\mathit{n}}_{\lambda }^{\mathit{y}}$] and ${\mathit{E}}_{\mathrm{xc}}^{\mathrm{LDA}}$[${\mathit{n}}_{\lambda }^{\mathit{x}}$]=${\mathit{E}}_{\mathrm{xc}}^{\mathrm{LDA}}$[${\mathit{n}}_{\lambda }^{\mathit{y}}$]. In contrast, for the true noninteracting kinetic energy it is proved that ${\mathit{T}}_{\mathit{s}}$[${\mathit{n}}_{\lambda }^{\mathit{x}}$]≠${\mathit{T}}_{\mathit{s}}$[${\mathit{n}}_{\lambda }^{\mathit{y}}$] for a general density without special symmetry, and corresponding inequalities are conjectured to apply as well to the exact ${\mathit{E}}_{\mathrm{xc}}$. Moreover, ${\mathit{T}}_{\mathit{s}}^{\mathrm{TF}}$ incorrectly gives the same value for its x, y, and z components.

The muonium atom ${\mathrm{\mu }}^{+}$${\mathit{e}}^{\mathrm{-}}$ is a simple system from which to gain information about the e-μ interaction both to test the existing theory of QED and to search for physics beyond the standard model. A systematic study has been carried out of the production and properties of thermal muonium from a fine silica powder. The velocity and angular distributions are examined, as well as the experimental conditions resulting in the optimum production rate. The particular properties of silica powder that give it its muonium-producing capability are investigated. These studies are carried out in the context of a diffusion model, the validity of which is examined.

The many-body theory of systems containing two types of charged light particles, like electrons and positrons, is investigated. The second quantized Hamiltonian, generalized Hartree-Fock equations and, in particular, the electron and positron Green’s functions and self-energy parts (optical potentials) are addressed. Exact properties of the latter quantities are discussed in some detail. A systematic approximation scheme that has been successful in the case of electronic systems is applied to the Green’s functions and self-energy parts of composite systems. Explicit working equations are derived.