We show that the steady-state photon-number distribution of the microscopic maser can be recovered using the standard macroscopic quantum laser theory. We introduce an appropriate limit of weak pump and weak photon damping to make the connection between the microscopic and the macroscopic quantum theory of laser operation. Simple analytic formulas describe the main features of the stationary photon-number distribution in the microscopic maser.

Techniques from the quantum theory of open systems (operations) are applied to the model of a kicked quantized cavity mode recently presented by Filipowicz, Javanainen, and Meystre [J. Opt. Soc. Am. B 3, 906 (1986)]. These techniques permit a straightforward discussion of atomic velocity profile in the model.

The master equation for a two-mode laser in a Λ-type three-level atomic system with arbitrary detunings has been derived. The effects of the detunings on the laser operation have been discussed. The asymmetry in threshold conditions for the two modes and the anomalous mutual support between the two modes in certain circumstances have been revealed. The former is due to the two-photon Raman-type resonance and the latter is attributed to the ac-Stark-shift effect.

A krypton discharge fitted with internal ohmic electrodes, excited by external rf electrodes, and perturbed by laser radiation at 785.5 nm, shows a strong optovoltaic signal that differs substantially from the conventional optogalvanic effect. The salient features of the discharge and the major characteristics of the optovoltaic signals are explored spectroscopically using a tunable diode laser that scans the 1$s_3$→2$p_3$ transition in krypton. Possible mechanisms and applications for this new type of signal are discussed.

We provide evidence for the universal behavior of the exponent characterizing the singularity of the Mayer fugacity series for the pressure of a fluid. As long as the two-body potential is positive but otherwise unrestricted, this exponent appears to be independent of the form of the potential and it is a monotonic, slowly increasing function, φ(D), of the dimensionality D of the system. A limited version of universality has previously been proposed by Poland [J. Stat. Phys. 35, 341 (1984)], restricted to hard, approximately spherical particles. Our results for φ(D) differ somewhat from those of Poland.

We have measured the frequency-dependent shear modulus of glycerol near the glass transition. The measurements, which covered three decades of frequency, probed the stress response of supercooled glycerol to small shear deformations. The shear response function has the same shape as the one obtained from ultrasonic experiments. Combined with previous measurements of ultrasound and specific heat, this result suggests that a single relaxation mechanism is responsible for such diverse phenomena as volume, shear, and enthalpy relaxations of the supercooled liquid of glycerol.

Ion density fluctuations are studied in a diffusion-controlled argon plasma containing, as a dilutant, two electron-attaching species, carbon dioxide, and sulfur hexafluoride. A glow discharge tube is used in this experiment; electrical probes and digital spectral analysis are our principal diagnostic and analytical tools. It is found that the system becomes increasingly unstable as the concentration of the electron-attaching species is increased. Nonlinear mode-mode couplings have been identified and the coupling coefficients for these interactions have been computed. Turbulent fluctuations are observed to have pronounced three dimensionality with distinct axial and azimuthal behaviors. The power spectra of these fluctuations are composed of many discrete modes and follow a P(w)∝$w^{\mathrm{-}n}$ trend with 3<n<5. The importance of changes in the total discharge pressure is dependent on the electron-attachment cross section of the dilutant species. From these results we show that the ionization instability is probably responsible for the observed phenomenon.

Time-resolved measurements of Ti xxi–Ti xix x-ray line spectra from an ohmically heated plasma with neon puffing in the JIPP-T-II-U tokamak were made with a high-resolution crystal spectrometer. The spectral data were analyzed by the use of a collisional radiative model which includes the cascade contributions from highly excited states as well as the recombination processes. We have fitted the observed spectra with synthetic calculations taking all the possible lines into account. From the intensity ratios of the satellite lines to the resonance line, the electron temperature $T_e$ was obtained every 20 ms. The result indicates that the plasma is in an ionizing phase at the beginning, reaches nearly an equilibrium around 80 ms, and then turns into a recombination phase, thereafter following the decrease of the electron temperature. The observed intensity ratios $I_x$/$I_w$ and $I_y$/$I_w$ were always found to be more than twice as large as the theoretical ones. The discrepancies increased in the later period of the plasma after $T_e$ decreased, in contrast to the result by Bitter et al. [Phys. Rev. A 32, 3011 (1985)], who found large discrepancies in the early phase of the discharge when $T_e$ was low. However, the experimental data of $I_z$/$I_w$ are in good agreement with calculations when we include the inner-shell ionization of Li-like ions. We investigated the contribution of ion-ion charge-exchange processes on the ion abundances and the line intensities.

We report measurements of Rayleigh-Brillouin spectra of ${\mathrm{SF}}_6$-He mixtures at moderate pressures. Kapral and Desai’s translational hydrodynamic theory [Chem. Phys. 3, 141 (1974)] describes the data in the hydrodynamic regime. We found a transition regime in which the He partial pressure is small.

A Lorentz gas interacting with a Lennard-Jones (LJ) potential and obeying classical equations of motion has been simulated by the molecular-dynamics method. A system of 255 Ar particles and one ${\mathrm{H}}_2$ molecule at a reduced Ar density 0.413 and temperature 2.475 is simplified by allowing the ‘‘argon’’ to have infinite mass, and the hydrogen molecule interacts with Ar atoms via the LJ potential. The simulated incoherent dynamic structure factor $S_s$(Q,ω) for the hydrogen molecule, which is corrected for the rotational states, is found to be in reasonable agreement with the experimental data of Egelstaff et al. (unpublished). One-parameter phenomenological model calculations are also compared to these data.

Three-photon excitation and multiphoton ionization techniques have been used to measure self-broadening for several resonance lines in xenon and krypton. Tabulations of widths and shifts of the xenon lines at 146.9, 129.6, 119.2, and 117.0 nm were made for pressures between 50 and 900 Torr. Similar measurements were made for the krypton resonance line at 116.5 nm. For pressures less than 500 Torr the widths were found to be in reasonable agreement with theoretical results, which were extrapolated into regions of concentration where the criteria for their validity are at best questionable. We have also found the lines to be shifted to the high-energy side of the unperturbed line. For four of the five lines studied, the blue shifts increased nearly linearly with increasing pressure. In the four cases where the shift could be measured the ratio of shift to width was close to (1/2. Our experimental technique is very simple, but it has yielded what we believe to be the first resonance broadening data based on absorption under conditions where there is strong trapping of the resonance radiation.

Results from computer molecular-dynamics simulations of pure water over a temperature range from 80 °C down to -30 °C are reported. The principal emphasis is on the nature of the translational diffusive motion of water molecules as deduced from quasielastic neutron scattering (QENS) experiments. The behavior of the QENS translational linewidth as a function of momentum transfer, q, is determined up to q=5.0–6.0 A${̊}^{\mathrm{-}1}$ and compared with experimentally derived linewidths up to q=2.0 A${̊}^{\mathrm{-}1}$ at several temperatures. Conclusions drawn from these comparisons reinforce those from earlier molecular-dynamics studies which found that self-diffusion in water takes place in a fairly continuous fashion in contrast to that implied by a random jump diffusion model. This is true even though that model does give a good description of recent high-quality QENS data.

Invoking the formalism known from second-order phase transitions and thermodynamics, we analyze the step structure obtained at transitions to chaos in dynamical systems or where Cantor sets evolve in general. As examples, we treat the skew tent map analytically and Arnold’s sine map numerically, but the presented formalism employed for embedding dimension d=1 is readily extended to higher dimensions. We outline the scaling behavior for the counting, the measure, and higher moments. In particular, we consider the crossover exponent ν which enters the scaling functions and for the measure is related to the critical exponent β and fractal dimension D. We emphasize that the general presence of a multifractal structure results in a value of ν which depends on from which moment it is defined, and deduce the saturation value of ν in the high-moment limit. Also, we derive the connection to thermodynamical functions as pressure, entropy, and escape rate. Finally, we examine the scaling behavior of the moments and scaling relations for exponents when either a ‘‘ghost’’ field or noise is introduced as a conjugated field involving the critical exponents α, γ, and δ as well as the crossover exponent μ.

Problems related to the definition of a Hopf bifurcation in the presence of noise are discussed in terms of three physical observables: the correlation functions, the power spectra, and the statistical densities. Of these, only the statistical density exhibits a distinct noise-induced transition. For a specific definition, only postponements are observed in analog simulator experiments with a Brusselator subject to white and colored noise on the control parameter. A recent prediction due to Lefever and Turner [Phys. Rev. Lett. 56, 1631 (1986)] is qualitatively tested.

We demonstrate by means of several examples that an easily calculable measure of algorithmic complexity c which has been introduced by Lempel and Ziv [IEEE Trans. Inf. Theory IT-22, 25 (1976)] is extremely useful for characterizing spatiotemporal patterns in high-dimensionality nonlinear systems. It is shown that, for time series, c can be a finer measure for order than the Liapunov exponent. We find that, for simple cellular automata, pattern formation can be clearly separated from a mere reduction of the source entropy and different types of automata can be distinguished. For a chain of coupled logistic maps, c signals pattern formation which cannot be seen in the spatial correlation function alone.

The effect of a weak electric field E on the cubic blue phases (BP’s) of cholesteric liquid crystals is considered. A Landau model, modified to include the uniaxiality induced by the field, is used. It is shown for space groups $O^8$ and $O^2$, which are believed to characterize BP I and BP II, respectively, that a free crystal will orient itself such that the field is parallel to a fourfold axis (a 〈001〉 direction), in agreement with experiment. For $O^5$, the stable orientation would be with the field parallel to a threefold axis (a 〈111〉 direction). In addition, in the presence of the field, there is (for all three cases) an induced birefringence. There are also shifts in the wavelengths of the Bragg reflections, and the cubic unit cell is distorted by a field in a 〈001〉 (〈111〉) direction into one having tetragonal (trigonal) symmetry. The ratio of the cell dimensions parallel and perpendicular to the field, the induced birefringence, and the wavelength shifts are, to lowest order, quadratic in E as expected from symmetry considerations. These results provide additional evidence for the generally accepted assignment of $O^8$ ($O^2$) for BP I (BP II), and for ruling out an $O^5$ structure for the observed BP.

This paper examines the effect of diffusive interactions, and the correlations they create between particles, on Ostwald ripening. The effect accounts for a persistent discrepancy between theory and experiment, in which the distribution of particle sizes has been more broad and flat than mean-field theory predicts. A new model system is proposed to study the problem, and a hierarchy of equations derived from it is expanded in powers of the square root of the volume fraction. The time devlopment of correlations is analyzed through an unusual perturbation theory. The resulting differential equations are solved numerically and compared with experiment.

We investigate theoretically dynamical aspects of the optical Freedericksz transition in nematic liquid crystals. Specifically, we analyze (1) the existence and stability of a sequence of higher-order longitudinal modes past the Freedericksz transition, (2) effects due to transverse correlations of the molecular orientation, and (3) the effects of thermal noise on the stability of the spatial modes. Higher-order longitudinal modes are studied both in the weak-anisotropy limit, in which case the problem reduces at steady state to a sine-Gordon equation, and in the general case, using a combination of analytical and numerical methods. They can be excited by the influence of internal fluctuations. Transverse correlations are shown to lead to the existence of transverse inhomogeneities (‘‘kinks’’) of the direct-angle distribution that can appear even under plane-wave illumination.

We consider an interacting fermion system in jellium. The particle-particle interaction is taken as a screened Coulombic one. The behavior of the ground-state energy per particle as a function of the screening and the interparticle distance $r_s$ is obtained. The density of states at the Fermi level as a function of the Wigner-Seitz distance and the screening parameter is calculated. In all the cases considered in this work, the localization of the particles in the system is obtained in a natural way in the low-density region, in agreement with Wigner’s prediction. Our results, obtained using as state function an expansion of periodic functions, are compared to the usual plane waves and to similar calculations with the same potential.

We consider the Markovian evolution in phase space of a distribution of particles subject both to a regular external field and to stochastic forces whose transition probabilities are Lévy stable densities. An integro-differential equation is derived which naturally generalizes the Fokker-Planck equation much as the stable densities generalize the normal. Its compact expression employs a new notation of vector fractional derivatives. Solutions are obtained for equilibrium conditions as well as for field-free and harmonically bound particle forces. The real-space Smoluchowski-equation limit of the Fokker-Planck equation is also generalized. It is suggested that the general evolution equation and stable densities may describe statistically the strange or fractal behavior of turbulent systems in the neighborhood of their critical points in phase space, with generally noninteger-order derivative laws governing the turbulent diffusion.