The inhibition of atomic-phase decays by squeezed light, and consequent line narrowing, is reexamined for the case of finite-bandwidth squeezing, as produced in the output of a degenerate parametric amplifier. The extension of previous work to incorporate the effect of nonwhite, or colored, noise is accomplished via an adjoint equation, which gives the time evolution of a matrix functional of the incoming field. Simple equations for atomic variables are derived in which noise operators are defined so as to commute with each other and with all other quantities. This facilitates the reduction of a purely quantum-mechanical problem to a classical problem, solvable by classical stochastic-approximation methods. In particular, small-noise-approximation methods and simulations are carried out for a wide range of parameters describing the squeezed-field input. The method of simulation is extended to the computation of correlation functions and spectra for a realistically achievable set of parameters, with consideration given to reflections of the input in the emitted light. The fundamental effect is confirmed, and modifications to previous results are given.

The effects of the cavity damping on the phenomenon of collapse and revival in the population inversion of an atom in a two-photon process are investigated by using the dressed-atom approximation. Explicit results are given for a field initially in either a coherent or a two-photon coherent state. The cavity damping is expected to have more significant effects on two-photon transitions because the vacuum-field Rabi frequency for two-photon transitions is smaller than that for single-photon transitions.

The first-passage times for a steady-state ring laser with a strong coupling and a detuning from resonance and for a laser with an injected signal have been studied. For a nonzero detuning the potential barrier surmounted by the system during the transition is shown to effectively increase because of the helical form of the trajectory.

A density matrix that describes the superposition of number eigenstates with thermal light is presented, and its matrix elements are calculated. The maximum information that this beam can transmit is compared with the maximum information that can be transmitted (i) by coherent signals in thermal noise and (ii) by coherent signals with random phase, in thermal noise.

We discuss a novel type of optical instability, which leads to the spontaneous formation of a stationary spatial structure, instead of to the onset of oscillations or pulsations. A passive system is contained in an optical cavity, to which we add two lateral mirrors. Under appropriate conditions, diffraction of radiation can induce the onset of a transverse-stripe structure in an initially uniform plane-wave field configuration. In this paper, we consider the case of a homogeneously broadened two-level system. The model on which our analysis is based is derived from the Maxwell-Bloch equations in the paraxial approximation, using the mean-field limit and assuming a large Fresnel number. We show that, with respect to the bistability parameter C, the threshold of the spatial instability coincides with the bistability threshold for absorptive, resonant optical bistability. The spatial instability requires, however, a detuned configuration and can arise both in the absence and presence of bistability. In the latter case, it can occur both in the lower and in the upper branch of the steady-state curve. The instability is caused by competition between different transverse modes, which realize a situation of spatial coexistence, different from the state of temporal coexistence which characterizes the spontaneous oscillations that arise from the previously known multimode instabilities. Finally, we discuss some points relevant for an experimental observation of this phenomenon.

The parameters of the linear instability to oscillatory convection (critical Rayleigh number, onset frequency, and others) are calculated for the experimentally common situation of rigid, impermeable boundaries, both near and away from the degenerate (codimension-2) bifurcation with stationary convection. This gives all linear coefficients of the standard and degenerate-amplitude equations. The small-Lewis-number limit is explicitly calculated. Wave-number and frequency jumps are confirmed in the vicinity of the codimension-2 point.

Recent experiments by A. H. Thompson, A. J. Katz, and R. A. Raschke [Phys. Rev. Lett. 58, 29 (1987)] have demonstrated that, when mercury is injected into a porous material, the electrical resistance of the sample decreases in a stepwise manner, with a power-law distribution of step sizes. Here we present computer simulations and a theoretical analysis of this process based on the model of invasion percolation. The simulations are consistent with the prediction that the number N of resistance steps greater in size than a given ΔR should scale as (ΔR${)}^{\mathrm{-}\lambda }$, with λ given in terms of the conduction exponent t and correlation-length exponent ν by 3ν/(t+3ν). This gives λ∼0.58, somewhat smaller than the experimental value 0.81 given by Thompson, Katz, and Raschke. It is argued that neither the resistance jumps themselves nor the hysteresis and long relaxation times observed in the experiment provide evidence against the application of percolation theory to fluid displacement in porous media. From the viewpoint of computer simulation, it is suggested that measurement of the exponent λ may be a good way of obtaining the value of the conduction exponent t.

This paper reports relative-line-intensity measurements of the n=3 to n=2 transitions for O v, F vi, and Ne vii in an electron density range of (4–9)×${10}^{12}$ ${\mathrm{cm}}^{\mathrm{-}3}$ in a tokamak plasma. Large discrepancies were found between the experimentally measured and theoretically computed values. The discrepancies are due to inaccuracies in the computations of the electron collision strengths from the 2$s^2$ and 2s2p levels to the 2s3p levels, using either the R-matrix method or the distorted-wave approximation.

When a fluid in a porous medium attempts to displace one which is more viscous, an initially flat boundary between them is unstable and fingers of the inviscid liquid penetrate the other. We model the medium numerically using a lattice of capillary tubes of random radii. Previous studies by one of the authors (P.R.K.) have already shown that the displacement is compact, but that the boundary between the two fluids is fractal. In this paper we study the distribution of velocities normal to the interface. We find that the distribution is consistent with the hypothesis that, for a system of size L, $L^{f\left(\alpha \right)}$ sites have velocities scaling as $L^{\mathrm{-}\alpha }$. The scaling function f(α) is measured and its variation with the viscosity ratio and randomness of the medium is found.

March and Murray derived a nonlocal theory of the charge displaced in a nonrelativistic electron gas by a weak, local potential V(x), using the density-matrix theory. The present work, based on the one-electron Dirac relativistic wave equation, generalizes their result to take account of the finiteness of the velocity of light. As examples, when V(x) is slowly varying the linearized version of the relativistic Thomas-Fermi theory of Vallarta and Rosen is recovered, while for weak but localized V(x) the nature of the Friedel oscillations far from the scattering center is derived.

Earlier investigators have shown that the free energy of an ideal gas in the ultrarelativistic (UR) regime of parametrized relativistic classical mechanics (PRCM) is different from the free energy calculated with use of the standard theory of relativistic classical mechanics (RCM). These differences do not become significant until very high temperatures are reached. Physical examples where the UR regime may be reached include the interior of stars, relativistic gas dynamics, and the first minute after the Big Bang. Of these, it is shown in the present paper that negligible differences are expected at realistic temperatures for relativistic gas dynamics and stellar models. This demonstration requires an evaluation of the PRCM and RCM free energies over a wide range of temperatures extending from the nonrelativistic limit to the UR limit. The greatest differences between PRCM and RCM are manifested in the density parameter of cosmological models. To study this effect, a general relativistic formalism is derived from variational principles within the context of PRCM. Scale factors and the age of Friedmann universes are calculated.

Detailed heat-capacity studies have been carried out in the vicinity of the smectic-C–smectic-I transition of two liquid-crystal compounds in the homologous series of racemic 4-(2’-methylbutyl)phenyl-4’-n-alkyloxybiphenyl-4-carboxylate (2M4PmOBC or mOSI). In contrast to the continuous smectic-A–hexatic-B transition found in many members of n-alkyl-4’-n-alkyloxybiphenyl-4-carboxylate (nmOBC) with symmetric and sharp heat-capacity anomalies, asymmetric and rounded ones are observed in the smectic-C–smectic-I transitions of both 2M4P8OBC and 2M4P9OBC.

Using molecular-dynamics simulations, we show that long-range three-body interactions have a negligible effect on the static and dynamical structure factors and on the transport properties of Kr gas.

The quasienergy spectrum of a particle in an infinite square well perturbed by a monochromatic external field is analyzed in terms of single- and double-resonance Hamiltonians. At small-enough perturbations the quasienergies are accurately given by those obtained from a single-resonance, integrable Hamiltonian. This indicates the existence of a local constant of motion and is a quantum manifestation of the Kolmogorov-Arnold-Moser theorem. At larger perturbations, the quasienergy spacing distributions are Poissonian for the single-resonance Hamiltonian. But for the double-resonance Hamiltonian, the distributions undergo a transition from Poissonian toward Wigner-like behavior when the perturbation is increased from a regime without resonance overlap to a regime with resonance overlap. This indicates the destruction of the local constant of motion through quantum-resonance overlap and its associated quantum number. It is a quantum manifestation of classical-resonance overlap.

We derive a dynamical equation for the stochastic motion of a vortexlike point disclination in thin smectic-C and -$C^{\mathrm{*}}$ liquid-crystal films. The inertial mass results from flow-induced distortions of the director structure in the core region, while the friction force is due to energy dissipation accompanying director rotations. The elastic force obtained from the curvature energy turns out to be negligible. The resulting dynamics is a Brownian motion, where the diffusion constant is much larger than for a comparable physical particle.

The kinetics of the gel-to-crystal phase transformation have been studied dilatometrically for lipid dispersions of 1,2-palmitoyl-sn-glycerol-3-phosphatidylcholine (DPPC). A new crystallization procedure is introduced in which the sample is first briefly quenched to form a small population of nuclei followed by jumping to temperatures at which negligible nucleation takes place but at which growth of nuclei occurs. Kinetic data obtained this way fit the classical Kolmogorov-Avrami relation very well over all measured times, up to 95% crystallization, but the effective dimensionality of the growing domains is only n=1.0–1.3. For the same system, differential scanning calorimetry shows that the data for the crystal-to-gel phase transformation are well fit with n∼1.1 and the data for the gel-to-ripple phase transformation are well fit with n∼0.8. Among the different possible causes of the small value of n for the two transformations involving the gel and crystal phases, the most viable focuses upon circular domains growing within each bilayer and the finite-size effects present in particular geometry of lipid dispersions. The fact that the gel-to-ripple transformation has a pronounced one-dimensional character accounts for its n value being even smaller.

We have studied the effect of electric fields on the blue phase III (BPIII) of chiral liquid crystals. A temperature–electric-field phase diagram is presented and the behavior of the BPIII selective reflections over this diagram is shown. The selective reflection consists of a broad peak situated on a sloping background; we argue that the background may be a remnant of additional structure at lower wavelength. A comparison of our data with three models for BPIII structure is made.

The scattering matrix, differential cross section, and total cross section for supramicrometer-size nematic droplets in a polymeric matrix are derived in the anomalous-diffraction approach. Scattering patterns are calculated in detail for three different nematic-director configurations: one characteristic of a droplet in a strong external field, the other characteristic of a droplet outside the field in the case of normal surface anchoring, and the third characteristic of an isotropic droplet with a surface-induced nematic layer. The results, which are presented graphically, indicate strong dependence of the diffraction patterns on wavelength and droplet structure. The possibilities of determining droplet size and nematic-director structure from experimental light scattering data are discussed. Special attention is paid to the possibility of the detection of the surface-induced nematic ordering.

The bouncing-ball problem was studied both experimentally and numerically. A qualitatively new behavior—so-called ‘‘self-reanimating’’ chaos—was found. In the experiment this behavior can be regarded as fully chaotic, but treated as regular motion (a cycle of large period) in the analytical approach.

The Gaussian and ‘‘uniform-gas’’ approximations to the Hartree-Fock exchange energy are demonstrated to arise from special cases of a generalized Padé approximation to the first-order density matrix. This fact enables one to use various numerical quadratures for approximating the exchange energy. The resulting formulas include both nonlocal and local (Dirac formula) approximations.