The multiphoton single-atom Dicke Hamiltonian in the dipole and the rotating-wave approximations is shown to reduce to the one-photon single-atom Dicke Hamiltonian via an approximate linearization process. For the special case of the Jaynes-Cummings Hamiltonian, it is shown that it is possible to derive a linearized form that is exactly equal to the original Hamiltonian.

Coincident 205-eV electrons resulting from the double ionization of argon by electron impact have been measured for incident energies from 400 to 2200 eV. The two 205-eV electrons are produced by knockout of an argon 2p electron followed by 205-eV LMM Auger decay of the 2p vacancy. The cross section near threshold is an order of magnitude larger than at higher energies. In addition, an angular correlation is observed for low incident energies. The two electrons are emitted preferentially at a large angle to each other. The results suggest strong electron correlation in this process.

An operator identity which allows the wave operator for N particles interacting pairwise to be expanded as products of operators in which fewer than N particles interact is given. This identity is used to derive appproximate scattering wave functions for N-particle continua that avoid certain difficulties associated with Faddeev-type expansions. For example, a derivation is given of a scattering wave function used successfully recently to describe the three-particle continuum occurring in the electron impact ionization of the hydrogen atom.

In examining the decay of photon-produced Be 1s2$s^2$np${(}^1$P), n=2,3, we discovered that the vastly predominant decay mode is to the final excited ionic states ${\mathrm{Be}}^{+}$ 1$s^2$np, rather than the ground state. For n=2, the 2p ion accounts for 95% of the total production, with ${\mathrm{Be}}^{+}$ 1$s^2$3p the other main contributor. For n=3, 3p is predominant, again with a very small fraction of 2s. The result for n=2 occurs as a consequence of the similarity between the 2s and 2p radial wave functions of the excited state, which leads to a cancellation in the amplitude for transition to the 2s ground state.

Cross sections for electronic excitation of ${\mathrm{H}}_2$O by low-energy electrons have been studied using the Schwinger multichannel method. Differential and integral cross sections for excitation of the (3$a_1$→3${\mathrm{sa}}_1$${)}^3$$A_1$ dissociative state are reported for impact energies of 12, 15, and 20 eV. A comparison of the calculated integral cross sections with emission measurements for OH ($A^2$${\Sigma }^{+}$) produced via dissociative electron-impact excitation of ${\mathrm{H}}_2$O in this energy range is encouraging.

Relativistic electron-impact ionization cross sections have been calculated for ${\mathrm{Au}}^{68+}$. Direct ionization cross sections were computed using a relativistic distorted-wave method. Relativistic distorted-wave electron collisional excitation cross sections and detailed relativistic radiative and Auger rates were calculated in order to determine the contribution of excitation-autoionization processes. Because radiative channels are the predominant decay modes for highly charged heavy ions, the effects of excitation-autoionization processes were expected to be small for ${\mathrm{Au}}^{68+}$. However, we found that these processes enhance the direct ionization cross sections by a factor of 4. This enhancement may be observed in experiments on the electron-beam ion trap in the near future.

A new light-induced drift effect is discussed in which a white-light source separates a gas mixture containing a single optically active (absorbing) species and a buffer gas which does not interact with the light. A three-level model with one upper level and two closely spaced lower levels is used for the active atoms, and strong collisions with the more abundant surrounding buffer gas atoms are assumed. The intensity spectrum in the vapor (including the effects of hyperfine pumping), and the resulting drift velocity are calculated as a function of optical depth into the vapor.

We have calculated photoelectron energy spectra for ionization of H(1s) by subpicosecond pulses with wavelengths 608 and 616 nm and with maximum intensity 1.2×${10}^{14}$ W/${\mathrm{cm}}^2$. The main features of the recently measured spectrum (at 608 mm) are reproduced.

A π-phase jump in the Stokes wave, which is responsible for Raman soliton formation, has been clearly detected by heterodyne phase detection with the use of two independent Stokes pulses.

An experiment has been carried out in which two pairs of light beams produced by down conversion in two nonlinear crystals driven by a common pump were mixed by two beam splitters, and the coincidence rate for simultaneous detections of mixed signal and idler photons was measured. It is found that the down-converted light carries information about the phase of the pump field through the entanglement of the down-converted photons with the vacuum.

We study the dynamics of a Morse oscillator subjected to periodic impulsive forcing. The system is governed by an area-preserving map that is factored explicitly into the product of two orientation-reversing involutions. The symmetry lines of these involutions are determined analytically. We discuss the organization of periodic and homoclinic orbits by symmetry and classify each according to the symmetry lines it visits. Finally, we generalize some of our findings to a larger class of impulsively driven Hamiltonian systems.

This paper presents a theoretical discussion of fractal growth. The distribution of growth probabilities on the evolving surface of many self-similar systems can be interpreted by a scaling or multifractal formalism. The extremities of the fractal contain the newest material from which further growth is likely to occur. A spatially fixed point in this peripheral region will quickly become screened, or shielded by the addition of new material nearby. The probability of growth from a chosen site will therefore decrease. We give a quantitative description of this process. We introduce the concept of length-scale-dependent exponents and predict that the active zone of the structure is determined by the q=1/2 moment of the probability measure. We also discuss the behavior of the most screened portions of the fractal, and the idea of time correlations in the growth.

The dynamic properties of large, sparsely connected neural networks are investigated. The input connections of each neuron are chosen at random with an average connections per neuron C that does not increase with the size of the network. The neurons are binary elements that evolve according to a stochastic single-spin-flip dynamics. Similar networks have been introduced and studied by Derrida, Gardner, and Zippelius [Europhys. Lett. 4, 167 (1987)] in the context of associative memory and automata. We investigate cases where some of the neurons receive inputs only from external sources and not from the network. These inputs may be random or uniform. The relationship between the geometric properties of the networks and their collective dynamic behavior is studied. Macroscopic clusters as well as internal feedback loops appear when C>1. However, the dynamic feedback is weak as the length of the typical loops is of the order of ln N. As a result, cooperative long-time behavior appears only at a value of C, C=$C_0$, that is higher than unity. The cooperative behavior is manifested by the existence of two distinct equilibrium phases with opposite magnetizations. In addition, when the inputs are uniform they determine uniquely the state of the network, thus destroying its bistability. Only at a higher value of C, C=$C_1$>$C_0$, a large fraction of the neurons is completely screened from the dynamic influence of the inputs, leading to a bistable behavior even in the presence of the inputs. These results imply that the performance of these networks as input-output systems may depend critically on the degree of connectivity.

We formulate and describe a renormalization-group transformation for classical λ${\phi }^4$-field theory on a lattice. The main idea is to divide the angle variables of the oscillators into the fast ones (large momenta) and the slow ones (low momenta) and to average over the fast ones. This results in an effective Hamiltonian for the remaining slow modes, which can be compared with the starting Hamiltonian. We derive fixed-point conditions and obtain a scaling law for those classical solutions for which the renormalization step can be iterated. There is a striking resemblence between our classical treatment and the analogous procedure in quantum field theory, which we discuss in some detail.

Nonperturbative integral equations are developed variationally for two-particle bound states in spinor and scalar quantum electrodynamics. The equations are solved numerically in the massive case and analytically in the massless case. The coupling constant is varied in order to study the bound states in the ultrarelativistic region.

We have experimentally investigated the behavior of a driven nonlinear electrical resonator over a large region of its control parameter space. If one regards the various responses of the resonator as different ‘‘phases’’ and constructs a ‘‘phase diagram’’ in the system control parameter space, many intriguing regularities become apparent. At drive frequencies far below the system’s resonant frequency, there exists a series of regions which are bounded by contours that mark the successive bifurcations in a period-doubling route to chaos. There are geometrical regularities in the size and location of these regions, and we suggest empirical scaling laws to describe these features. The appearance of period doubling and chaos in nonlinear systems that are driven far below resonance can have considerable practical significance and, in the empirical observations that are given in this paper, are a step in understanding the global parameter-space behavior of nonlinear systems.

A low-temperature expansion of an isotropic, spatially frustrated lattice model with nearest-neighbor, second-, and third-nearest-neighbor interactions is presented. The zero-temperature states of this model are known exactly. For some regions of parameter space there is an infinity of zero-temperature states, although the ground-state entropy per spin is zero at zero temperature. In general one expects fluctuations at finite temperature to break the degeneracy on the zero-temperature-state manifold. When the zero-temperature states are regular or periodic, it is possible to characterize them and to apply the low-temperature expansion to break this degeneracy in a rigorous way. In the present paper we carry out such a calculation. However, we also have examined regions of parameter space where the degenerate states are irregular. A method is proposed that permits one to resolve between degenerate irregular states. It consists of low-temperature expansion in successively larger local clusters or fragments of the allowed zero-temperature states. In principle one need have no a priori knowledge of the symmetry of the zero-temperature state. However, there results a packing problem that involves maximizing the number of clusters with optimal free-energy density. In some cases we have been able to solve this problem, while for other parts of the phase diagram we have made conjectures that have yet to be confirmed by rigorous calculations.

Coupled integral equations are developed variationally and solved numerically for the two-particle bound-state problem in quantum electrodynamics. The ansatz incorporates explicit photon degrees of freedom, and the resulting equations, when perturbatively reduced, yield the correct perturbative ${\alpha }^4$ coefficients. The results are of interest as they may be applied to the large spin-dependent effects in the highly relativistic bound systems of quantum chromodynamics.

We develop the path-integral formalism as applied to non-Markov stochastic processes in order to allow us to study the effects of colored external noise on a physical system. The system we initially consider consists of a Langevin equation ẋ=-V’(x)+ξ, where ξ is a Gaussian noise with zero mean and correlator 〈ξ(t)ξ(t’)〉=(D/τ)C(‖t-t’‖/τ), τ being the noise correlation time. Starting from the Langevin equation, we obtain a path-integral representation for probability density functions on the infinite time interval -∞<t<∞, and show how in certain cases a simple representation also exists in terms of a sum over paths on a finite time interval. The weighting factor for paths in this latter case consists of an exponential factor which is a generalization of that originally found by Onsager and Machlup but also contains nontrivial boundary terms depending on the initial preparation of the system.