Two anharmonic (harmonic) oscillators were coupled by an exponential nonlinearity. The temporal development of the phase-space distance indicates alternating regular and stochastic motion as a function of the coupling parameter and the energy.

The energy of a monolayer of surfactant on a surface is calculated as a function of the orientation of the surfactant tails. The structure is determined by a competition between the spacings preferred by the polar heads and nonpolar tails. As a function of the head-tail mismatch, we find a region of no molecular tilt, and one of uniform tilt. In the tilted state, solitonlike defects resembling micellar clusters are stabilized by entropy or finite-size effects.

A natural oscillator subjected to periodic forcing with adjustable frequency and amplitude may behave aperiodically or be entrained to oscillate with an integer multiple of the forcing period. Entrainments occur in subsets of the frequency-amplitude plane and are well understood for very small forcing amplitude. We investigate the mechanisms by which entrainments are terminated at moderate amplitudes and support our theory by numerical experiments on a model chemical oscillator.

By considering afresh the three-dimensional diffusion of an asymmetric top molecule, new statistical cross-correlation functions are reported using computer simulation. Off-diagonal elements exist directly in the laboratory frame (x,y,z) of the tensor cross-correlation function between a molecule’s Coriolis acceleration, 2ω×v at time t and its own angular velocity ω at t=0. Here v is the molecule’s center-of-mass linear velocity. This is the first clear evidence that the historically popular theory of rotational diffusion is in need of development at a fundamental level to involve directly the linear velocity v.

Analytical expressions for the static structure function for a polydisperse Percus-Yevick fluid with Schulz (gamma) distributed particle diameters have been obtained. Results obtained with the expression for selected width factors and particle densities are presented.

Theoretical formulas for the length, velocity, and acceleration forms of the electric-dipole matrix element within the adiabatic hyperspherical coordinate representation are presented. The length and acceleration formulas are used to calculate the photoionization cross section for He up to 1.0 a.u. above threshold and the photodetachment cross section for ${\mathrm{H}}^{\mathrm{-}}$ up to 0.35 a.u. above threshold. Length- and acceleration-form results for the dipole oscillator strengths for the discrete He transitions, 1sns${(\mathrm{}}^1$$S^e$)→1smp${(\mathrm{}}^1$$P^o$), where n=1, 2, and 3 and m=2, 3, and 4, are also presented. The accuracy of the length- and acceleration-form adiabatic hyperspherical coordinate approximation results is discussed.

We report an experimental and theoretical study of the forced autoionization of the doubly excited Ba 5d7d ${(}^1$${\mathrm{D}}_2$) state which lies ∼200 ${\mathrm{cm}}^{\mathrm{-}1}$ below the ${\mathrm{Ba}}^{+}$ 6$s_{1/2}$ ionization limit. In zero field the 5d7d state perturbs the 6snd ${(}^1$,3${\mathrm{D}}_2$) series by configuration interaction. The essential notion of forced autoionization is that applying a field of >2.5 kV/cm converts the 6snd states into a Stark continuum and the 5d7d state appears as an autoionization resonance. In this study we compare the zero-field configuration-interaction parameters with those obtained for the interaction of the 5d7d state with the structureless ‖m‖=1 field-induced continuum and find rather similar values, thus confirming the utility of forced autoionization as a spectroscopic tool. In addition, we report a systematic investigation of the interaction of the 5d7d state with the highly structured ‖m‖=0 Stark continuum.

We report measurements of photoelectron angular distributions for the 3${\sigma }_g^{\mathrm{-}1}$ and 2${\sigma }_u^{\mathrm{-}1}$ photoionization channels of ${\mathrm{N}}_2$ from their thresholds up to 35 and 37.5 eV, respectively. The asymmetry parameter β for the 2${\sigma }_u^{\mathrm{-}1}$ channel exhibits a broad dip in the range hν∼27–32 eV that was recently predicted theoretically to arise from shape-resonance-enhanced continuum-continuum coupling between the 3${\sigma }_g^{\mathrm{-}1}$ and 2${\sigma }_u^{\mathrm{-}1}$ ionization channels. The β parameter for the 3${\sigma }_g^{\mathrm{-}1}$ channel exhibits a prominent feature at hν∼23 eV, which is tentatively attributed to the autoionization of a doubly excited valencelike state. Otherwise, the gross shape of the 3${\sigma }_g^{\mathrm{-}1}$ β curve is in good agreement with independent-electron calculations, which realistically reflect the influence of the well-known ${\sigma }_u$ shape resonance in this channel.

The dynamic properties of the 4f subshell in atomic ytterbium were studied experimentally with the aid of synchrotron radiation and theoretically in the relativistic random-phase approximation (RRPA). Satisfactory agreement between experiment and theory was obtained for the β parameter, the R(4$f_{7/2}$/4$f_{5/2}$) branching ratio and the relative partial cross sections between 17.5 and 100 eV. This indicates that 4f photoionization is described well in the RRPA model. The properties of the 6s subshell were measured between 17.5 and 50 eV. In the resonance region 5p→5d the population of the three main exit channels 6s, 4$f_{7/2}$, and 4$f_{5/2}$ were recorded in detail between 24 and 31 eV using the constant-ionic-state technique. For the approximately 15 resonance states similar populations of all channels were found. The 5p resonance structure was also calculated using a limited number of interacting channels in the multichannel quantum-defect theory.

The consequences of having state-specific diagonal transition matrix elements on the interaction of a two-level system with a laser field and a static electric field are examined within the dipole and rotating-wave approximations. A finite difference between the permanent dipole moments can result in the appearance of subsaturating ancilliary fringes flanking the usual Lorentzian transition resonance. The requisite conditions for a two-level system to exhibit an oscillatory line shape are discussed. These fringes arise from the essential transparency of the system to the field at prescribed intensity-dependent frequencies.

Processes such as dielectronic recombination or excitation-autoionization, which involve doubly excited states, are important for understanding the kinetics of laboratory plasmas. Theoretical studies of these processes require knowledge of Auger as well as radiative decay rates for the intermediate states involved. We have applied Stieltjes moment theory techniques to the problem of calculating autoionization widths for the (3l3l’) doubly excited states of ${\mathrm{Kr}}^{25+}$ (sodiumlike krypton). Configuration-interaction wave functions were used to describe the resonances as well as the continuum. We have explored the effects of intermediate coupling, configuration mixing, and orbital relaxation on the calculated autoionization rates.

Calculations are presented of the limitations imposed by radiation trapping on the electron spin polarization produced in an alkali-metal vapor by optical pumping in a large magnetic field. It is found that electron spin polarizations of 90% are possible with Na densities up to ${10}^{19}$ atoms/${\mathrm{m}}^3$ and ground-level relaxation times of 150 μs in a large magnetic field using a cylindrical geometry of radius 7.5×${10}^{\mathrm{-}3}$ m.

Correlation times of mode amplitudes in a multimode cw dye-laser system have been measured using intracavity absorption spectroscopy. The dependence of the mode-correlation times on the spectral power density in the laser cavity has been investigated in detail. At low spectral power densities, surprising discontinuities are observed and interpreted as dynamical instabilities in the laser system. At high spectral power densities, the mode-correlation time approaches a constant value. These observations are described by a system of two nested, self-referential feedback loops explaining the behavior of the laser system. The resulting model is discussed within the concepts of generalized multistability and presumably chaotic behavior.

A technique for efficiency enhancement in free-electron-laser and ‘‘ubitron’’ amplifiers (where the ubitron is essentially a free-electron laser operated at electron beam energies less than 500 keV) is analyzed which makes use of both tapered wiggler and axial guide magnetic fields. A set of model equations is derived which describes the coupling between an ensemble of electrons and the radiation field. The analysis is fully three dimensional, and treats the propagation of an electron beam of fi- nite cross-sectional area through a loss-free cylindrical waveguide in the presence of a helically symmetric wiggler field and an axial guide magnetic field. The model equations are solved numerically, and substantial enhancements in the interaction efficiency are found for a variety of choices of the model parameters. The efficiency enhancement is observed to be a sensitive function of both the degree of taper in the wiggler and axial magnetic fields as well as the point at which the taper is begun. In order to illustrate the physical mechanism underlying the efficiency enhancement, a modified pendulum equation which describes the interaction is derived from the orbit equations under a set of idealized assumptions, and used to construct a small-signal theory of the efficiency enhancement.

We extend our theoretical formalism describing how one strong classical wave and one or two weak quantum-mechanical waves interact in a nonlinear medium to the ‘‘two-photon two-level’’ model. In this model, field transitions between two levels not connected by an electric dipole occur by means of a two-photon transition using off-resonant intermediate levels. This model has many similarities with, as well as significant differences from, the corresponding one-photon two-level model that has been treated in the previous papers in this series. The theory yields the first detailed calculation of the two-photon resonance fluorescence spectrum, as well as the complete set of four coefficients that describe the quantum theory of two-, three-, and four-wave mixing.

A numerical study of the effect of laser-frequency fluctuations on dispersive optical bistability shows a strong dependence on the strength and correlation time of the noise. Both the stationary-state characteristics and switching times are studied, and a qualitative explanation is provided for some of the numerical results.

A microscopic correlation function expression for the signal in four-wave mixing is developed. Both stationary and transient (i.e., photon-echo) experiments with coherent or incoherent radiation fields are considered. In general, these observables are described by an eight-point correlation function of the dipole operator involving two particles, and the signal cannot be written as an amplitude squared. Conditions under which the correlation function may be factorized into a product of two four-point, single-particle correlation functions are specified. In this case the conventional approach, based on calculating a nonlinear polarization and substituting it as a source in Maxwell’s equations, is justified. However, in the presence of long-range spatial correlations in the sample (e.g., near critical points) the conventional formulation breaks down and the present theory should be used.

We propose the use of a laser model in which the single-mode approximation is introduced for the electric field but not for the atomic variables. We show that our improved single-mode model is in good agreement with the exact steady-state solution for a reasonable range of experimentally relevant parameters well beyond the limits of validity of the mean-field approximation.

In this paper we describe how a quantum system consisting of a single extended coordinate q in a double-well potential V(q), which interacts with a dissipative environment, may be systematically reduced (‘‘truncated’’) to an equivalent two-state system interacting with a modified environment. Although we concentrate on Ohmic dissipation, the method which we present is also applicable to other types of environmental spectral densities. The truncation scheme is applicable if there exists a wide separation of energy scales in the problem; we discuss the specific conditions which the system and environment must satisfy before such a scheme can be implemented. Our method proceeds by calculating the effects of the high-frequency environmental modes on the bare tunneling matrix element for transitions between the two wells. We are left with an equivalent two-state system with a renormalized tunneling matrix element, interacting with the remaining low-frequency environmental modes. The renormalized tunneling matrix element is calculated using path-integral techniques in a semiclassical approximation. Explicit results are given for a quartic double-well potential in the underdamped and overdamped regimes.

The very recent experimental results on the new phenomenon of resonant activation in current-biased Josephson junctions [M. H. Devoret, J. M. Martinis, D. Esteve, and J. Clarke, Phys. Rev. Lett. 53, 1260 (1984)] are completely accounted for via a theoretical approach which settles the problem of determining the rate of escape of a highly inertial Brownian particle from a potential well in the presence of a radiation field. To get this very satisfactory agreement with experiment a theory was developed, the main features of which are as follows. (1) The subtle problem of elimination of irrelevant variables is dealt with by devoting special attention to the case where the time scale of the system of interest is not well separated from that of the irrelevant variables. (2) A perturbation approach is used which, in the absence of stochastic force, is proved to coincide with the well-known method of multiple time scales. (3) It is assumed that the process of excitation-relaxation within the well is much faster than the process of escape from the well itself. The theory of this paper predicts analytically the frequency position for the maximum escape rate in terms of a suitable renormalized anharmonicity parameter α. In the conditions of the aforementioned experiment this theory predicts the shift from the natural frequency to be 2α (with an agreement with experiment of ±1%). Furthermore, theory predicts that if the friction is lowered, a new phenomenon takes place: the shift of the maximum from the natural frequency is reduced to α. Analytical predictions on the friction region where this transition takes place are made.