We have calculated the energy spectrum of a highly excited atom in parallel electric and magnetic fields. The eigenvalues were obtained by semiclassical quantization of action variables calculated from first-order classical perturbation theory. For the field strengths studied, the electron moves on a Kepler ellipse whose orbital parameters evolve slowly in time, and first-order perturbation theory reduces the problem to just one degree of freedom. Action variables were calculated from perturbation theory and the eigenvalues were obtained by semiclassical quantization of the action. The semiclassical analysis leads directly to a correlation diagram which connects the eigenstates of the Stark effect to those of the diamagnetic effect. A classification scheme for the eigenstates is proposed. Comparison with first-order degenerate quantum perturbation theory verifies the accuracy of the semiclassical treatment.

We consider first a dielectric medium of identical two-state atoms coupled by the radiation field to an initially excited atom outside the dielectric. From the Schrödinger equation follows a delay-differential equation describing how the atom interacts with the dielectric by virtual photon exchanges. In the macroscopic limit of a continuous distribution of atoms in the dielectric, we derive a simpler delay-differential equation in which a Fresnel reflection coefficient appears. We apply our results to a model of an atom in a multimode Fabry-Perot resonator, and obtain a general delay-differential equation for the probability amplitude of the initially excited state. This equation predicts well-known Rabi oscillations when the round-trip photon propagation time is negligible compared with the inverse of the Rabi frequency and the mirrors are highly reflective. For low mirror reflectivities we recover Purcell’s prediction that the emission rate is enhanced by the cavity Q factor. When the photon bounce time is large compared with the inverse Rabi frequency, Rabi oscillations do not occur. We discuss the Ewald-Oseen extinction theorem from the standpoint of quantum mechanics.

By constructing a vector model we study the coherent dynamics of a special three-level quantum system–one with equal detunings and equal Rabi frequencies. This three-level problem can be fully related to a two-level problem. We find that complete population depletion can be achieved even in the case of constant nonzero detunings when the three-level system is prepared initially in the common level of the two transitions. Complete population depletion with constant detunings can also occur in other odd-number multilevel systems. An explanation in terms of an equivalent resonant excitation is presented.

As a continuation of a previous paper [J.-M. Liu, Z. Phys. B 57, 85 (1984)], the present paper is about the dynamical threshold phenomena in the system of a single-mode one-photon laser driven by an external coherent field. The values for the dynamical threshold exponents and amplitudes near the various thresholds are theoretically predicted. As shown, the characteristic time goes to infinity as the control parameters of the system approach each of these thresholds, and the influence of the existence of the absorbing atoms in the laser cavity on the dynamical threshold phenomena in the system is definite.

Calculations are performed for stimulated Raman scattering in ${\mathrm{H}}_2$ in the transient regime. The production of anti-Stokes radiation depends strongly on phase matching in the dispersive medium, and a predictive theory requires at least two spatial dimensions to describe the process.

The pump amplitude fluctuation of a current-driven semiconductor laser can be suppressed to below the ordinary shot-noise level by ‘‘high-impedance suppression.’’ As a result of this pump-fluctuation suppression, the output of a current-driven semiconductor laser exhibits amplitude squeezing in the frequency region below the cavity bandwidth. The noise equivalent circuits and the quantum-mechanical Langevin equations are derived and discussed for clarifying the difference between an ordinary laser oscillator with shot-noise-limited pump fluctuation and a constant-current-driven semiconductor laser.

Single-particle dynamics of electron motion through a free-electron-laser cavity with axial guide field is presented. Equations governing the trajectories in the absence of radiation are obtained, and significant departures from the results of earlier work are discussed. Linearized gain in the presence of radiation is derived. Comparison with previous studies reveals (i) good agreement with results and (ii) gain enhancements at hitherto unreported frequencies.

The temporally stationary state of Burgers fluid between walls is discussed in the inviscid limit under a class of external, random forcing. The force and the fixed boundaries are shown to pose determinate restrictions on the fluid motion in the large, and drive the Burgers fluid to construct, and to alternate between, a few characteristic structures for dissipation. A mean-field approximation is presented with its inviscid-limit closed solutions for average profiles in the stationary state. The solutions are not unique and reproduce, though with varying accuracies, the mentioned structures of the fluid motion. Results of numerical runs are also reported, and their statistics is shown to admit reconstructions on this picture, confirming further the existence of these quasistationary structures and the itinerant motion of the fluid among them.

The shear viscosity is predicted to increase considerably because of domains in critical fluids quenched into the unstable or metastable region. This is because domains can be easily deformed and broken by shear, resulting in great increase of the surface area, near the critical point. The excess viscosity due to domains, Δη, can be of the same order as the viscosity in the one-phase region in the weak-shear case. It exhibits marked non-Newtonian behavior in the strong-shear case. Predictions are also made on a normal-stress effect due to domains.

We performed a nonequilibrium molecular-dynamics (MD) study of thermodiffusive cross coupling in an argon-krypton liquid mixture, near the krypton’s triple point. We carried out nonequilibrium MD simulations, employing the MacGowan-Evans algorithm and subtraction technique with two sets of values for the external fields, to locate the onset of the nonlinear region. We also checked consistency with our equilibrium Green-Kubo calculations. Our results are in reasonably good agreement with previous MD computations and show that nonequilibrium and Green-Kubo methods have comparable efficiency, both yielding the same values for the cross phenomenological coefficients, as in the direct transport case.

We present numerical solutions in the singular (‘‘critical’’) region of the hypernetted-chain (HNC) equation for a model fluid system described by a pair potential consisting of a highly repulsive core and an attractive well. In contrast to the behavior of real systems, we find that the isothermal compressibility ${\kappa }_T$ does not actually diverge on the critical isochore ρ=${\rho }_c$ as the temperature T is lowered toward the critical temperature $T_c$. Rather, there exists a locus of temperatures $T_s$(ρ), parametrized by density ρ [with $T_s$(${\rho }_c$)=$T_c$], on which ${\kappa }_T$ remains finite, but below which no physical solutions to the HNC equation exist. This behavior breaks down at densities near triple-point conditions, where ${\kappa }_T$ has a true divergence at a low enough temperature. There is a striking similarity between certain aspects of this critical behavior and that of the Percus-Yevick equation, for which comparison can be made to the analytic solution available for the case of the sticky hard-sphere potential.

We report the first Monte Carlo study of the average critical number of bonds per site $B_c$ for three-dimensional continuum systems. The results show that for a system of spheres the dependence of $B_c$ on the soft-shell to hard-core ratio can be mapped onto the site-percolation–bond-percolation transition in lattices. For a system of very long cylinders, $B_c$ appears to be a dimensional invariant. It is predicted that for any continuum system the above dependence will be equal or weaker than that of a system of spheres.

Using the generalized Langevin model and analytical expressions for the scaling behavior and fractal dimension of atomic trajectories, liquid argon is studied over a range of temperatures and densities. The observed Richardson coefficient α is shown to change continuously between values of α=0 and α=1 as the trajectory length is increased, with the limiting value of α=1 (Brownian motion) occurring for trajectories of length t≊${10}^{\mathrm{-}9}$–${10}^{\mathrm{-}8}$ sec. The present study also indicates that long-time memory effects are evident in the approach of the Richardson coefficient to this limit.

We consider a general class of non-Markovian processes defined by stochastic differential equations with Ornstein-Uhlenbeck noise. We present a general formalism to evaluate relaxation times associated with correlation functions in the steady state. This formalism is a generalization of a previous approach for Markovian processes. The theoretical results are shown to be in satisfactory agreement both with experimental data for a cubic bistable system and also with a computer simulation of the Stratonovich model. We comment on the dynamical role of the non-Markovianicity in different situations.

Ullersma’s model consistently describes the quantum-mechanical damped harmonic oscillator. Proper limiting processes in the initially reversible solutions lead to irreversible behavior. It is shown that the irreversible solutions can directly be derived from a field version of the discrete Ullersma Hamiltonian H (H→$H_F$). In the ground state of the system the phonon occupation number of the oscillator does not vanish. Therefore, these ‘‘bare’’ phonons cannot be interpreted as ‘‘physical’’ quanta or particles. By suitable canonical transformations, the bare-field description is transformed into a physical description ($H_F$→$H_{\mathrm{ph}}$), which allows the definition of physical particles and which is characterized by a renormalized frequency, a screened interaction between oscillator and bath, and a symmetry of position and momentum operators. The physical description is closely related to the rotating-wave approximation of the original model. The relaxation behavior and the equilibrium properties of the different descriptions are discussed and compared.

We consider a purely dissipative spin system operating far from thermodynamic equilibrium. We prove that a coarse graining for short-wavelength modes is obtained near criticality by performing a center-manifold reduction of fast-relaxing modes. The spin systems considered are realizations of a time-dependent Ginzburg-Landau model. Agreement with renormalization-group derivations is obtained. Neutron scattering cross sections for a magnetic material in the dynamic critical case are calculated making use of the center-manifold reduction. Experimental measurements of static spin autocorrelations are used to obtain the distribution of fast modes about the center manifold. Making use of this information, predictions are made on neutron scattering for magnetic materials coupled to a heat bath near a dynamic critical point. The existence of a center manifold determines scaling relations between the strength of the statistical forcing field and the spin-correlation length. Thus, the relevance of a time-dependent experiment under far-from-equilibrium conditions becomes apparent inasmuch as such an experiment can lead to the elucidation of the nature and strength of the statistical noise.

We present a defect model for melting of discotic liquid crystals. It is explicitly shown that a discotic liquid crystal permeated by an equilibrium density of unbound screw and transversal edge dislocation loops behaves like a nematic liquid crystal in the so-called N+6 phase. We derive the dislocation part of the free energy and calculate the interaction energy between two parallel transversal edge dislocations. We then argue that dislocation-mediated melting of discotics into the N+6 phase implies strong anisotropic scaling with ${\nu }_{\perp }$=2${\nu }_{?}$. Some consequences follow about the critical behavior of Frank elastic constants previously derived.

A two-body-interaction model characterized by the scattering length a is applied to study the thermodynamic and magnetic properties of nonrelativistic interacting systems of spin-(1/2) particles in the presence of an external homogeneous magnetic field under the assumption that the particles obey generalized statistics of order l. Here one assumes that the occupation number of an energy state can take values 0,1,2,3,...,l and no more, where l is an integer greater than unity. Exact expressions for thermodynamic and magnetic properties due to the generalized nature of the statistics are obtained and the characteristic departure of the present results from those of the Fermi-Dirac case are pointed out. Variation of thermodynamic properties with the interaction parameter ${\mathrm{av}}^{\mathrm{-}1/3}$ is also obtained.

Crises in a two-well forced oscillator of Duffing type are studied with an analog simulation. Its features are discussed with the aid of return maps and phase portraits. Two types of boundary crisis in a strange attractor following the Feigenbaum route to chaos are found. One is associated with a hopping between two strange attractors and is confirmed with the presence of 1/f noise spectrum. The other is associated with a hysteresis jump. A borderline of differentiating these two characters is also indicated.

Efficient algorithms have been used to grow large (4×${10}^6$ site) diffusion-limited aggregation (DLA) clusters on two-dimensional (2D) square lattices. As the clusters grow larger, their envelope grows, from a more or less round shape characteristic of small clusters, through a diamond shape characteristic of clusters containing about ${10}^5$ sites, into a cross shape. Results from about 25 clusters indicate that the exponents describing the length l and width w of the four major arms vary continuously with M (the cluster mass) over the range ${10}^3$${10}^6$. We find that the effective exponent ${\nu }_{?}$=dln(l)/dln(M) increases systematically from 0.585 to 0.61 at the highest mass. This may be consistent with a limiting value of (2/3) (as found for uniaxially biased DLA in two dimensions) but only with large corrections to scaling in our range of M. The exponent ${\nu }_{\perp }$=dln(w)/dln(M) decreases systematically, to about 0.48 at M=4×${10}^6$. Our results are consistent with an asymptotic (scaling) fractal geometry for square-lattice DLA but suggest that these fractals are neither self-similar nor homogeneous.