We discuss semiclassical expansions for the off-diagonal thermal kernel of quantum systems with a nonuniform, time-independent, magnetic field. In the process, we derive a new equation for the WKB approximation for such systems. In particular, we provide recursion relations and a diagrammatic method for calculating explicitly the coefficients in these expansions. As an illustration we present the off-diagonal coefficients up to order ${\hslash }^3$, and the on-diagonal coefficients up to ${\hslash }^6$ for a uniform magnetic field. We also give the on-diagonal coefficients up to order ${\hslash }^4$ for a nonuniform field.

A computer simulation technique is used to calculate hydrogen spectral lines emitted by a plasma. These calculations are used to study ion dynamic effects on the line profiles. Results are obtained for Lyman-$\alpha$, Layman-$\beta$, and Lyman-$\gamma$ lines, and comparisons are made with experimental results and with other theoretical methods.

The spatial and temporal bifurcations of a ring of coupled, discrete-time, nonlinear oscillators are studied. The model displays many of the phenomena observed in diffusively coupled, nonlinear, chemical oscillators which can possess complex dynamics when isolated. The low-order bifurcation diagram of the discrete-time model may be computed analytically and shows how in-phase and out-of-phase solutions arise and undergo further bifurcations to quasiperiodic or chaotic states. Spatial bifurcations (pattern formation) accompany the temporal bifurcations and the results indicate how some of these processes occur. The phase diagram possesses self-similar scaling features associated with the higher-order periodic states. The model should prove useful in identifying the analogous phenomena in physical systems.

The steady-state, spherically symmetric Fokker-Planck equation of Brownian motion is solved in an infinite homogeneous medium surrounding a perfectly absorbing sphere. The solution is obtained by expanding the distribution function in terms of Burnett functions. It is shown that the final solution consists of an asymptotic mode found earlier, and a set of transient modes that decrease exponentially with the distance from the center. Our numerical results in the so-called $L_1{P}_1$ approximation [S. Waldenstrøm, K. J. Mork, and K. Razi Naqvi, Phys. Rev. A 28, 1659 (1983)] indicate that the transient modes have only a small influence in the determination of the coagulation coefficient.

The molecular dynamics of the $R$ and $S$ enantiomers of fluorochloracetonitrile (HCFC1NC), and of the racemic mixture, are investigated with computer simulation. Some novel single-molecule rotation-translation cross-correlation functions are reported in a moving frame of reference defined by that of the principal molecular moments of inertia. Two off-diagonal elements of these cross-correlation matrices have an equal and opposite time dependence for the two enantiomers and vanish for all $t$ in the racemic mixture. The application of an external electric field to the chiral liquid generates laboratory-frame cross-correlation functions between the molecular center-of-mass translational momentum and the angular momentum of the same molecule. These cross-correlation functions are, therefore, seen in standard spectroscopic investigations of the molecular liquid state. As the intensity of the external field is increased, the following transient and field-on equilibrium effects become observable in the laboratory frame of reference: (i) Orientational rise transients are opposite in sign for the two enantiomers and vanish in the racemic mixture. (ii) These transients are field dependent, the dependence being qualitatively, but not quantitatively, that given by simple diffusion equations such as the Debye equation. (iii) At field-on equilibrium, the Grigolini decoupling effect is confirmed, i.e., the envelope of the oscillatory angular-velocity autocorrelation function decays more slowly than the field-off autocorrelation function at equilibrium as the external electric field strength is increased. (iv) The orientational fall transients are accelerated considerably with respect to the time dependence of the equivalent field-off orientational autocorrelation function. These results are interpreted with reduced-model theory, with use of Kramers equations with nonlinear potential terms.

We discuss, within a unified renormalization-group (RG) framework, the onset of chaos appearing in the $1-a{\left|x\right|}^z$ map for real $z\ge 1$. In particular, we study with some detail the criticality associated with the $k\to \infty$ limit of the $p^k$ bifurcation sequences [$p=2, 3, \mathrm{and} 4$, which correspond, respectively, to the $R^{*k}$, ${\mathrm{}\left(\mathrm{RL}\right)\mathrm{}}^{*k}$, and ${\left({\mathrm{RL}}^2\right)}^{*k}$ Metropolis-Stein-Stein sequences]. The critical points $a_p^{*}\mathrm{}\left(z\right)\mathrm{}$ monotonically increase, for all values of $p$, from $a_p^{*}\mathrm{}\left(1\right)\mathrm{}$ [$1\le a_p^{*}\mathrm{}\left(1\right)<2\mathrm{}$] to 2 as $z$ increases from 1 to ∞. The $z$ dependence of ${\delta }_p\mathrm{}\left(z\right)\mathrm{}$ for $p=2\mathrm{}$ [${\delta }_2\mathrm{}\left(z\right)\mathrm{}$ monotonically increases as $z$ increases from 1 to ∞] is different from that associated with $p>\mathrm{}2\mathrm{}$ [${\delta }_p\mathrm{}\left(z\right)\mathrm{}$ diverges in $z\to 1$ and (possibly) $z\to \infty$ limits, presenting a minimum in the neighborhood of $z=2\mathrm{}$]. The present RG recovers, for both $a_p$ and ${\delta }_p$ and all values of $p$, the exact asymptotic behaviors in the $z\to 1$ limit. It suggests, in the $z\to \infty$ limit, the (possibly exact) asymptotic behaviors $a_p^{*}-2\mathrm{}\propto \frac{1}{z}$ and ${\delta }_p\propto z$.

A recent paper of Horáček and Sasakawa [Phys. Rev. A 28, 2151 (1983)] is discussed. Firstly, we show that their formulation of the theory for multichannel scattering should be corrected. Then, after a slight modification, their continued-fractional one-channel formalism remains applicable to the multichannel case as well. Secondly, an alternative multichannel method is suggested based on a similar idea. It represents the solution of the corresponding coupled integral equations in terms of the matrix continued fractions.

Atomic $L$- and $M$-shell ionization cross sections by protons have been calculated in the plane-wave Born approximation for ${}_{79}{}^{}{}_{}{}^{}\mathrm{Au}$ and ${}_{92}{}^{}{}_{}{}^{}\mathrm{U}$ with incident energy from 0.1 to 3 MeV with use of relativistic and nonrelativistic Hartree-Slater wave functions. These results are compared with those from the screened hydrogenic model to study the effects of relativity and wave functions. The relativistic and wave-function effects are found to operate in opposite directions. For $M_{1,2,3}$-subshell cross sections, severe cancellations occur between these two factors.

We present a new approach to rotational-vibrational excitation of molecules by slow electrons, incorporating the shape resonance, the dipole interaction, and the interference between their amplitudes. Excellent agreement is found with the high-resolution differential-cross-section data in CO for vibrational excitation and the simultaneous excitation of individual rotational branches. Accurate state-to-state integral cross sections are given for CO at the resonance energy of 1.8 eV.

Wavelength and lifetime measurements for the fine-structure components of the $1s2s2p{}_{}{}^4{}_{}{}^{}P_{}^o{}_{}{}^{}-1s2p^2{}_{}{}^4{}_{}{}^{}P$ multiplet in lithiumlike Ne VIII have been made using foil excitation of a fast-ion beam. The results are compared with recent theoretical calculations and with previous measurements for other ions of the same isoelectronic sëquence. An apparent discrepancy between theory and experiment for the $1s2p^2{}_{}{}^4{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ lifetime is removed.

Accurate Hylleraas-type wave functions have been used to calculate oscillator strengths for the transitions $mP-nD$, $m,n<~5$, in heliumlike ions with $Z=3-7\mathrm{}$. The uncertainty of the results estimated from the numerical convergence is less than 0.1% for most of the transitions studied. The results can be used to obtain reliable interpolated oscillator strengths for ions with $Z>~8$.

Using microwave resonance techniques, we have measured Na $d-f$ intervals from $n=9-12\mathrm{}$ at frequencies of up to 116 GHz. The measured intervals are an order of magnitude more precise than previous $d-f$ interval measurements, with typical uncertainties of 100 kHz. These measurements are a necessary part of improved quantum-defect measurements in Na and determine the $\mathrm{nd}$ fine-structure intervals a factor of 5 more accurately than the previous work. Finally the $\mathrm{nf}$ fine-structure intervals are determined to be 3%-4% less than the hydrogenic interval for $n$ as low as 9.

The undamped Bloch equations are shown to have a more general analytic solution which includes the famous self-induced-transparency solution of McCall and Hahn, and the nonadiabatic excitation solution of Allen and Eberly as special cases. A generalized area characteristic for a laser pulse of modulated amplitude and frequency of the forms of hyperbolic secant and tangent is given. It resolves the difficulty of the previous area concept in the presence of frequency modulation. The solution provides an exact analytic result for the amplitude- and frequency-modulated pulse of any area.

It is shown that the field emitted by a free-electron laser (FEL) in the low-gain regime exhibits antibunching over a wide range, for an initial Poisson distribution of probability amplitudes. We also investigate the variance of the momentum coordinate, and find the FEL state to be squeezed.

It is shown that the Lagrange multipliers, which vanish at the initial time, can be eliminated in the Robertson method by using a special noncanonical density operator.

The nonlinear propagation of an electromagnetic wave along an external magnetic field in a uniform plasma is reconsidered in order to include the combined effects of the relativistic-mass and ponderomotive-force nonlinearities. The results of previous works on this subject are improved significantly.

The evolution equation accounting for effects of diffusion and recombination is transformed into a similarity equation in one, two, and three dimensions. This equation does not fulfil the Painlevé criterion and thus cannot be directly classified, or its properties analyzed, in general terms of its singularities. A particular similarity solution can, however, be constructed. It allows for a description of the evolution of plasma configurations of physical significance.

It is shown that nonlinear-mode coupling of drift waves can generate magnetostatic fluctuations in an inhomogeneous magnetized plasma. The growth rate of the parametric instability is estimated for typical tokamak parameters.

Nonlinear coupling of a coherent electrostatic ion-cyclotron (EIC) wave with finite amplitude compressional Alfvén modulations can give rise to localized EIC wave packets. Criteria for the wave localization are obtained analytically.

A model for a three-component solution is considered in which the bonds of a square or cubic lattice are covered by molecules of types $\mathrm{AA}$, $\mathrm{BB}$, and $\mathrm{AB}$. The ends of molecules near a common lattice site interact with energies ${\epsilon }_{\mathrm{AA}}$, ${\epsilon }_{\mathrm{BB}}$, and ${\epsilon }_{\mathrm{AB}}$. It is shown there is no demixing transition in the model if ${\epsilon }_{\mathrm{AB}}<~\frac{({\epsilon }_{\mathrm{AA}}+{\epsilon }_{\mathrm{BB}})}{2}$.