An analytical steady-state distribution for the phase difference ψ in a correlated spontaneous-emission laser (CEL) is derived based on the amplitude and phase equations of a CEL. This distribution is shown to be an excellent approximation to that obtained from a numerical simulation of the complete set of CEL equations. In particular, the effects of amplitude noise on CEL operation are considered and it is shown that fluctuations in the relative amplitude are also noise quenched.

The theory of laser action in solid-state systems is reconsidered with emphasis on the role of the interaction between lasing impurity states and lattice vibrations. The influence of a strong electron-phonon coupling on threshold conditions and field dynamics is presented, taking into account the vibronic-level structure, and compared with the usual four-level scheme.

Gaussian pure states of systems with n degrees of freedom and their evolution under quadratic Hamiltonians are studied. The Wigner-Moyal technique together with the symplectic group Sp(2n,openR) is shown to give a convenient framework for handling these problems. By mapping these states to the set of n×n complex symmetric matrices with a positive-definite real part, it is shown that their evolution under quadratic Hamiltonians is compactly described by a matrix generalization of the Möbius transformation; the connection between this result and the ‘‘abcd law’’ of Kogelnik in the context of laser beams is brought out. An equivalent Poisson-bracket description over a special orbit in the Lie algebra of Sp(2n,openR) is derived. Transformation properties of a special class of partially coherent anisotropic Gaussian Schell-model optical fields under the action of Sp(4, openR) first-order systems are worked out as an example, and a generalization of the ‘‘abcd law’’ to the partially coherent case is derived. The relevance of these results to the problem of squeezing in multimode systems is noted.

The effective rate of a chemical reaction is a complex combination of purely chemical effects and of effects related to transport phenomena or, more generally, to the spatial degrees of freedom. This coupling is analyzed in the limiting case of almost ideal mixing, taking into account the spatiotemporal correlations of the turbulent velocity field. A weak-noise expansion permits the deduction of an effective eddy diffusivity which is a function not only of the statistical properties of turbulence but also of the chemical kinetics. An application to the problem of thermal ignition is outlined.

We report measurements of the intensity and linewidth of the light quasielastically scattered from a binary critical mixture of n-hexane and nitrobenzene along various constant-concentration paths. The agreement between the intensity data and the scaling theory for the static quantities, and of the linewidth data with the dynamic-mode coupling theory for the transport coefficients and for the decay rate of the order parameter, including background effects, is very good.

It is generally thought that equilibrium self-gravitating condensations of plasma must be electrically quasineutral. While this is true in the case of an atomic plasma, there is a realizable type of plasma in which it is not true. If the massive component of a two-component plasma consists of charged macroscopic solid grains for which the charge-to-mass ratio is of order √G , then self-gravitation and thermalization lead to substantial equilibrium charge separation. Within a thermalized gravitational condensation of this plasma, the scale height of the oppositely charged low-mass component is much larger than that of the grains. Consequently, the large-scale charge-to-mass ratio is also of order √G . There is evidence that an understanding of such condensations may be relevant to the understanding of galaxies.

Stochastic relaxation in underdamped nonlinear potentials driven by exponentially time-correlated noise is studied thoroughly by means of analog simulation. The experimental data reported herein should help to tie down future theoretical investigations. A novel dependence of the observed quantities on the noise correlation time τ is revealed: all of the quantities measured are a function of ${\tau }^2$. In particular, the escape rate in a quartic double-well potential decreases exponentially with increasing ${\tau }^2$. The relevant spatial spectral densities are also determined for both the monostable and the bistable quartic potential on varying τ. Previous theoretical predictions for the white-noise (τ=0) limit are thus checked. The frequency of the resonance peak is shown to shift depending on ${\tau }^2$. Finally, some effort has been paid at justifying theoretically the results obtained.

We numerically investigate statistical properties of short-wavelength normal modes and the spectrum for the Helmholtz equation in a two-dimensional stadium-shaped region. As the geometrical optics rays within this boundary (billiards) are nonintegrable, this wave problem serves as a simple model for the study of quantum chaos. The local spatial correlation function 〈${\psi }_n$(x+(1/2s)${\mathrm{\psi }}_{\mathrm{n}}$(x- 1) / 2 s)〉 and the probability distribution $P_n$(ψ) of wave amplitude for normal modes ${\psi }_n$ are computed and compared with predictions based on semiclassical arguments applied to this nonintegrable Hamiltonian. The spectrum is analyzed in terms of the probability P(ΔE) of neighboring energy-eigenvalue separations, which is shown to be similar to a Wigner distribution for the eigenvalues of a random matrix.

The asymptotic behavior of the solution to steady dendrite growth with isotropic surface tension is examined. The results show that (1) at far field (z→∞), the deviation of the nonisothermal dendrite from an Ivantsov &, where the eigenvalue ${\alpha }_1$ is within the interval (0,(1/2) and can be determined by the undercooling of the melt and (2) the asymptotic character of the dendrite at far field cannot be fully determined locally. It is also influenced by the behavior of the solution at the tip region. These results demonstrate that the conventional far-field boundary condition in which the difference between the dendrite and the Ivantsov paraboloid is vanishingly small is not correct. Moreover, the results also imply that for any finite surface tension linearization around the Ivantsov solution corresponding to zero surface tension may not be uniformly valid in the whole region (0≤z<∞). As a consequence, the conclusions drawn from the linearized system, such as the nonexistence of the steady solution and the ‘‘solvability condition theory,’’ are questionable.

Relative rotation rates for two-dimensional driven dynamical systems are defined with respect to arbitrary pairs of periodic orbits. These indices describe the average rate, per period, at which one orbit rotates around another. These quantities are topological invariants of the dynamical system, but contain more physical information than the standard topological invariants for knots, the linking and self-linking numbers, to which they are closely related. This definition can also be extended to include noisy periodic orbits and strange attractors. A table of the relative rotation rates for a dynamical system, its intertwining matrix, can be used to determine whether orbit pairs can undergo bifurcation and, if so, the order in which the bifurcations can occur. The relative rotation rates are easily computed and measured. They have been computed for a simple model, the laser with modulated parameter. By comparing these indices with those of a zero-torsion lift of a horseshoe return map, we have been able to determine that the dynamics of the laser are governed by the formation of a horseshoe. Additional stable periodic orbits, besides the principal subharmonics previously reported, are predicted by the dynamics. The two additional period-five attractors have been located with the aid of their logical sequence names, and their identification has been confirmed by computing their relative rotation rates.

We introduce a new family of aggregation models with constant interjection. In our models, the asymptotic distribution of particle mass, s, always follows a power law, P(≥s)∝$s^{\mathrm{-}\alpha }$, where (1/3≤α≤ 1) / 2 . It is clarified that this power law is realized by a balance of two effects, injection and aggregation.

The dimension of fractal sets, such as strange attractors, can be derived from near-neighbor information. This gives rise to practical algorithms to estimate the spectrum of Renyi dimensions from an experimental signal. In high-dimensional phase spaces they may also be very efficient. A proof of these methods is given, using a formalism of local scaling indices. We emphasize the restriction on the calculable range of q values imposed by the neighbor order. In connection with the normalization of the distribution of scaling indices we also discuss possible corrections due to the finite size of the set of data points.

Under certain circumstances, sidebranching in a dendrite may result from the selective amplification of noisy fluctuations in the tip region. This suggestion is based on numerical and analytical studies of the two-dimensional boundary-layer model with both kinetic and surface tension anisotropy. From the dynamical simulations, smooth steady fingers are observed above a critical anisotropy, below which the fingers are unstable. Noise added to a smooth steady tip gives sidebranching. A temperature estimate of the required noise indicates that thermal noise is a candidate. An analytic description of the response of the tail of the dendrite to a perturbation in the tip region is given and this analysis is compared to the numerical results. Comparison is also made to experiment as the undercooling and anisotropy are varied. Implications for the full model are discussed.

We present the extension to statistical mechanics of a mapping technique of the Wigner and Weyl kind, but based upon the coherent-state representation. The central theme is that of introducing an appropriate method for the evaluation of traces of unbounded operators.

In the resonant reactive scattering theory of Mundel, Berman, and Domcke [Phys. Rev. A 32, 181 (1985)], the overlap of a Morse continuum state and a Lanczos basis state appears in the expression of transition amplitude. In their study, recursion relations for Green’s functions in the Lanczos basis were used for computational efficiency. In this paper we derive new recursion relations specifically for the evaluation of overlap between the Morse continuum wave and Lanczos basis state that appears in the transition amplitude of resonant scattering. They are found to be simple to use with great accuracy.

Rigorous lower bounds to the electronic charge and momentum densities of an atomic system at the origin, ρ(0) and γ(0), respectively, by the expectation values 〈$r^{\alpha }$〉 and 〈$p^{\alpha }$〉, respectively, are given for positive and negative values of α in both cases, provided that the charge and momentum densities have a monotone decrement behavior, respectively. They allow one to give rigorous bounds to ρ(0) and γ(0) in terms of experimentally measurable atomic quantities such as the diamagnetic susceptibility, the Compton profile peak, and the electronic energy. In particular it is shown that ρ(0)≥(4 √3 π${)}^{\mathrm{-}1}$N〈${\mathrm{r}}^{\mathrm{-}2}$${\mathrm{〉}}^{3/2}$ with the charge density normalized to N, the number of electrons of the system. The quality and the asymptotic Z behavior of the bounds for neutral atoms (N=Z) are studied.

By employing the N-dimensional hypervirial equations with the Hellman-Feynman theorem to the more general case of a screened Coulomb potential, V(r)=-(a/r)[1+(1+br)$e^{\mathrm{-}2\mathrm{br}}$], the entire bound-state energy spectrum is obtained.

By using analytical self-consistent field functions in the model of Burch et al., we have constructed an exact analytical expression for the K-shell x-ray energy shifts for an additional 2p vacancy. The expression is used to judge the quality of the model.

Corrected values of photon-emission cross sections from collisions of protons (100–325 keV) with ${\mathrm{N}}_2$O are reported. The cross sections are for the 100–000 and 000–n00 (n=0,1,2) bands of ${\mathrm{N}}_2$O. The dependence of the cross sections on beam energy has not changed with the new values.

We have observed the polarization of Lyman-α radiation after the interaction of 70-keV protons with a thin tilted carbon foil. The circular polarization shows a sinusoidal dependence on the angle of tilt, whereas the components of linear polarization in the emitted radiation are found to be generally small. It is demonstrated that the polarization observed after the transmission through the foil at large angles of tilt extrapolates to the data obtained after the reflection of ions from the foil surface at grazing incidence.