With the help of numerical simulations using an extended Su-Schrieffer-Heeger-type Hamiltonian, the existence of solitary waves in a polyformamide stack is shown. Each formamide unit in the stack has three geometrical degrees of freedom during the time simulation. The passing of a solitary wave through the stack and its reflection at the end of the chain is shown. In addition, the collision of two solitary waves is discussed.

A comparison of dynamical theories and metastable states in regular and glassy (mean-field) spin models with underlying first-order-like phase transitions is made. We emphasize that for the glassy case, fluctuations probe the region in phase space where metastable states exist. This is contrasted to the situation for regular spin models. We physically interpret our results in terms of a dynamical instability of the paramagnetic phase in the glassy models. For the glassy case we conclude that as soon as metastable states exist, the mean-field model exhibits an ergodic to nonergodic transition where full ensemble averages are no longer equal to time averages.

The relation between quantum electrodynamics and (classical) stochastic electrodynamics is elucidated by means of a general construction which associates with every Gaussian quantum field (for example, vacuum-free fields or coherent states at zero or nonzero temperature) a classical random field, which in the case of quantum electrodynamics yields stochastic electrodynamics. The associated classical and quantum theories yield the same results for all nondisturbing (causally separated) field measurements. This is an additional classical characteristic of coherent quantum states which implies that Bell’s inequality is satisfied by quantum field measurements. Furthermore, stochastic electrodynamics is identified as the Wigner distribution of quantum electrodynamics. We point out that in these Gaussian states stochastic electrodynamics is more suitable as a classical model of the quantum field than is the Euclidean field, which results from applying Nelson’s stochastic mechanics to each field mode.

A nonlinear effect of convection on the diffusion-limited-aggregation (DLA) fractal is investigated by use of the real-space renormalization-group method. The renormalization-group equations are derived for two parameters: the diffusion constant on the interface and the Péclet number P^ representing a ratio of the convection effect to the diffusion effect. It is found that the correlation length ξ (limiting the validity of the self-similarity) diverges as ξ∼‖P^${\Vert }^{\mathrm{-}\nu }$, where ${\nu }^{\mathrm{-}1}$=ln(∂P^ ’/∂P^${)}_{\mathrm{P}\mathrm{^}=0\mathrm{}}$/lnb (b is a scale factor). The correlation-length exponent ν is approximately given by ν=d${\mathrm{}\left(0\right)\mathrm{}}^{\mathrm{-}1}$, where d(0) is the surface fractal dimension of the DLA. The aggregate is the DLA fractal on smaller length scales than the correlation length, but becomes a nonfractal structure on large length scales. The renormalization-group method is applied to the formation of solidification patterns in two cases: one is the case of an undercooled melt and the other the case in which the aggregate acts as a heat sink. In the undercooled-melt case the convection acts as a destabilizing force on the interface, but, for the aggregate with a heat sink, the convection acts as a stabilizing force. It is shown that the DLA fractal crosses over to one of the two distinct nonfractal structures depending on the direction of the heat flux.

We extend the partial resummation technique of Fokker-Planck terms for multivariable stochastic differential equations with colored noise. As an example, a model system of a Brownian particle with colored noise is studied. We prove that the asymmetric behavior found in analog simulations is due to higher-order terms which are left out in that technique. On the contrary, the systematic τ-expansion approach can explain the analog results.

The effects of dissipation on the transport of quasiparticles obeying the nonlinear discrete Schrödinger equation are studied. Dissipation is introduced via the standard stochastic Liouville equation and, for a molecular dimer, a closed integro-differential equation is derived for the time dependence of the probability difference at the two molecular sites. The equation is solved numerically in the general case and analytically in a certain limit involving weak nonlinearity and damping, and the solutions are used to describe the scattering spectrum. The integrability of the equations of motion is investigated and it is shown that the equations of motion do not possess the Painlevé property.

We have identified the four lowest bound states of ${\mathrm{Mn}}^{\mathrm{-}}$: 3$d^5$4s4$p^2$ ${}_{}{}^9{}_{}{}^{}P_j^{}{}_{}{}^{}$ ($E_A$=0.586,0.597,0.607 eV for J=5,4,3, respectively) and 3${\mathit{d}}^5$4${\mathit{p}}^3$ ${}_{}{}^9{}_{}{}^{}$S${\mathrm{°}}_4$ (${\mathrm{E}}_{\mathrm{A}}$=0.470 eV). The electric dipole oscillator strength connecting ${}_{}{}^9{}_{}{}^{}\mathrm{P}$ and ${}_{}{}^9{}_{}{}^{}\mathrm{S}$ ° is 0.343 (length) and 0.299 (velocity). Our energetic results include both relativistic and many-body effects. We find that a relativistic zeroth-order function involving open d and p electrons may characteristically involve over 100 configurations.

The Coulomb-Born approximation has been used to study the excitation of positive ions by heavy-particle impact. Slater-type wave functions are used for the ionic target states. This choice enables us to calculate the excitation rate coefficients between arbitrary initial and final states. We calculate the differential and total cross sections and alignment parameters for excitation of ${\mathrm{He}}^{+}$ ions from the ground state to the 2p state by proton impact. The alignment parameters for the projectile velocity range considered here are found to be positive in contrast to negative values of the corresponding parameters for electron-impact excitation of the same target states.

In a previous paper [Phys. Rev. A 35, 3945 (1987)] the Sturmian expansion of the irregular solution of the Schrödinger equation was considered. Here I consider the expansion of the regular solution.

An idealized model of an optical communication link in which identical sections of nonlinear attenuating fiber alternate with identical amplifiers is considered. Signal-to-noise ratios of chains of these elements for input squeezed and coherent light have been numerically evaluated. It is found that input squeezed light and nonlinear attenuators improve the signal-to-noise ratios with respect to coherent inputs and linear chains. In the case of three-photon attenuators, the noise and signal-to-noise ratio remain practically constant from certain elements of the chain. Moreover, the influence of the attenuation coefficient and the input mean photon number on the signal-to-noise ratios was considered, as well as chains with nonlinear amplifiers and chains in which the amplifier gain does not exactly compensate for the fiber attenuation.

The Lorentz group, which is the language of special relativity, is a useful theoretical tool in modern optics. It is shown that the SU(1,1) interferometer of Yurke, McCall, and Klauder can serve as an analog computer for Wigner’s little group of the Poincaré group.

We obtain the wave function in the coordinate representation of the one-mode squeezed states ‖ζ, α〉=exp(ζ${\mathit{a}}^{\mathrm{^}2}$-${\mathrm{\zeta }}^{\mathrm{*}}$${\mathit{a}}^2$)exp(α${\mathit{a}}^{\mathrm{^}}$-${\mathrm{\alpha }}^{\mathrm{*}}$a)‖0〉. The wave function is a displaced Gaussian with center and width depending upon the parameters α and ζ.

We study the experimental structure factor of liquid Pb using the modified hypernetted-chain equation. The dependence of the pair potential on the structural environment is related to the electron effective mass which changes discontinuously at the melting point while the pseudopotential remains invariant. A solid-phase pair potential derived from liquid-phase results gives good elastic constants, phonon data, and the low-temperature electronic specific heat, although based only on a local two-parameter pseudopotential.

Analytic forms are presented for velocity profiles in two-dimensional channel flow for a non-Newtonian fluid when the fluid is subject to a pressure gradient. The forms reduce to those of the Navier-Stokes theory, e.g., the Poiseuille form for the velocity profile, as the fluid tends to a Newtonian fluid. Therefore they are nonlinear generalizations of Poiseuille-type flow velocity profiles.

The frequency and linewidth of the longitudinal acoustic sound wave in propylene glycol were measured by Brillouin scattering. The relaxation rates obtained in the gigahertz frequency range are compared with the low-frequency specific-heat-capacity data in terms of the Vogel-Tamman-Fulcher law and the scaling law. The results for slow relaxation processes at the sub-$T_g$ region for propylene glycol are also presented.

S. Nosé [Mol. Phys. 52, 255 (1984); J. Chem. Phys. 81, 511 (1984)] has developed a form of molecular dynamics that generates the canonical ensemble. Since molecular-dynamics calculations are carried out at constant total linear momentum, we investigate the necessary modifications in Nosé’s theory when the constraint of constant total linear momentum is imposed. We show that Nosé’s theory can be modified so that it generates phase-space trajectories corresponding to a constant-momentum canonical ensemble with zero total momentum. We also present an exact treatment of the statistical mechanics of this constant-momentum canonical ensemble, including expressions relating averages to thermodynamic variables and formulas involving thermodynamic response functions which are often used in molecular-dynamics calculations.

Analytical expressions for the correlation of subsequent molecular displacements during diffusion along fractal networks are derived. On the basis of these relations, the NMR spin-echo attenuation due to anomalous diffusion in both constant and pulsed field-gradient experiments is determined.

According to a recent prediction by Badii and Politi [in Dimensions and Entropies in Chaotic Systems, edited by G. Mayer-Kress (Springer-Verlag, (Springer-Verlag, Berlin, 1986)], low-pass filtering of chaotic signals results in systematic errors in the determination of the attractor dimension. We show that in an experimental situation with the additional complication of small sample sizes of low resolution, the prediction still holds. The entropy $K_2$ appears to be unaffected by the filtering.

We take issue with several remarks made in a recent article by K. Kundu and P. Phillips [Phys. Rev. A 35, 857 (1987)].

In this response we clarify the remarks made by J. W. Haus and K. W. Kehr [Phys. Rev. A 37, 4522 (1988)] regarding the definition of the diffusion coefficient in the random-trapping model.