A new scheme for generating an amplitude-squeezed state is proposed. The photon-flux fluctuation of a semiconductor-laser output wave is measured with a quantum nondemolition (QND) detector, and is negatively fed back to the laser pumping current. The operator Langevin equations are derived by combining the quantum-mechanical analyses on the laser internal-external field fluctuations, the quantum nondemolition detector based on an optical Kerr effect, and a negative-feedback circuit. The output wave features a reduced photon number noise below the standard quantum limit, 〈(Δn^${)}^2$〉<〈n^〉, and an enhanced phase noise above that, 〈(Δψ^${)}^2$〉>(1/4)〈n^${〉}^{\mathrm{-}1}$, while the minimum uncertainty product is still preserved. The observed photoelectron statistics in a negative-feedback GaAs laser diode using a conventional p-i-n photodiode (not a QND detector) are shown to exhibit sub-Poissonian statistics with the variance 〈(Δn^${)}^2$〉apeq20.26〈n^〉. The measured photocurrent fluctuation spectral density is also indicated to be below the standard quantum limit by a factor of 0.2 (=-7 dB). The experimental results also confirm that such amplitude squeezing is only observed inside the feedback loop and cannot be extracted from the loop unless a quantum nondemolition detector is used.

A linearized theory of fluctuations for absorptive bistability based on the positive P representation is developed without adiabatic elimination of the atoms or the field. An analytic expression for the steady-state covariance matrix is derived from which the size of quantum-statistical effects can be estimated without restriction to the good- or the bad-cavity limit. When the atom and field relaxation rates are similar the intensity correlation function of the transmitted light exhibits an oscillatory relaxation associated with vacuum Rabi splitting.

We report an experimental and theoretical study of the optical piston, a consequence of the phenomenon of light-induced drift (LID), observed in binary mixtures of Na vapor and a buffer gas. Good agreement has been found between experiment and existing theory as far as the shape of the Na density profile in the piston is concerned. The piston velocity is anomalously low; this is accounted for by incorporating the effects of adsorption and desorption into the theory. Furthermore, we introduce a rate-equation model for LID which incorporates the fine and hyperfine structure of the level scheme of the Na absorbers; this gives insight into the sublevel velocity distributions and the nonequilibrium part of the total velocity distribution during LID.

The squeezing spectrum for a cavity field mode interacting with an ensemble of three-level ‘‘Λ-configuration’’ atoms by an effective two-photon transition is calculated. The advantage of the three-level Λ system as a squeezing medium, that is, optical nonlinearity without atomic saturation, has recently been pointed out by Reid, Walls, and Dalton. We predict perfect squeezing at the turning points for dispersive optical bistability and good squeezing for a range of other cases. Three-level ladder atoms interacting by an effective two-photon transition are also shown to give perfect squeezing in the dispersive limit.

By analyzing the functional equations governing N replication for real nonlinear maps on the (unit) interval (of order z), we have derived the asymptotic (N→∞) behaviors of the scaling constants α and δ, α(z)∼(2z${)}^{\left(N\mathrm{-}1\right)/\left(z\mathrm{-}1\right)}$, δ/${\alpha }^z$=(z-1)/(z-1/2). In addition, we have determined the limiting forms of the universal functions. The predictions are in excellent agreement with (separately compiled) numerical data over a wide range of z values and cycle structures.

A new method of calculating electric microfields in plasmas, based on density-functional theory (DFT), is presented. Strong-coupling effects, quantum effects, internal structure of the test particle, etc., are conveniently and rigorously treated. DFT is used to calculate the ion-electron and ion-ion pair distribution functions $g_{\mathrm{ie}}$ and $g_{\mathrm{ii}}$. These are then used to calculate the electron-screened electric field and the first- and second-order terms in the Baranger-Mozer (BM) formulation of the microfield probability function. When low-order BM fails for strongly coupled systems, a weighted summation of chainlike diagrams may be used for evaluating the all-order sum. We present low-frequency microfield calculations for neutral and charged test particles without structure, a neutral particle with H-like structure, and an aluminum ion immersed in a hydrogen plasma. We also consider the case of neutral and charged test points in an aluminum plasma and compare our results with apex. Our microfields differ significantly from the usual ones, and depend specifically on the nature of the plasma, as well as the nature and structure of the test particle. For increasingly classical weakly coupled plasmas our results fall into agreement with the existing microfields which depend essentially on the ratio (density${)}^{\mathrm{-}1/3}$/(Debye length).

The phase-space contraction for the systems under consideration corresponds to an asymptotic-center manifold functional dependence of the fast-relaxing variables, $X_f$,j’s, on the slowly-relaxing ones, the $X_s$,i’s. The propagation of perturbations along the center manifold is obtained from the Green-function sensitivity matrix. Scaling and self-similarity relations among the matrix elements are found. This fact allows for a simplification in the computation of the $X_f$,j-$X_f$,j and the $X_s$,i-$X_s$,i autocorrelations. The validity of the results is confirmed in two different contexts: (a) An analytical derivation of power spectra at the onset of periodic instabilities is performed. We demonstrate that in the infinite relaxation time limit for slow variables, the power spectra for all the $X_f$,j’s converge to the same distribution. This result is in accord with previous computations. (b) The power spectrum for a randomly driven anharmonic damped oscillator is computed at the asymptotic-center manifold regime and tested vis-a$aa—-vis previous plots exhibiting a very good agreement.

We obtain here an approximate, nonlinear Fokker-Planck-type equation which offers an improved model for two-dimensional nonequilibrium, bistable flows driven by exponentially correlated Gaussian noise. The new model accurately predicts the renormalization of the phase-space statistical densities P(x,v) with correlation time. The theory is tested for accuracy by both analog electronic and digital simulations of a damped oscillator with a bistable potential, driven by additive, colored noise. For large noise strengths, the improved theoretical scheme is applicable for small noise correlation times τ, but becomes increasingly better for small noise strengths where its accuracy extends even to large noise correlation times. The crossover to overdamped motion is also discussed.

Le Chatelier’s principle is discussed within the constrained variational approach to thermodynamics. The formulation is general enough to encompass systems not in thermal (or chemical) equilibrium. Particular attention is given to systems with multiple constraints which can be relaxed. The moderation of the initial perturbation increases as additional constraints are removed. This result is studied in particular when the (coupled) relaxation channels have widely different time scales. A series of inequalities is derived which describes the successive moderation as each successive relaxation channel opens up. These inequalities are interpreted within the metric-geometry representation of thermodynamics.

The van der Waals energy of a two-dimensional array of tilted alkyl chains is evaluated numerically by summing the contributions of pairs of ${\mathrm{CH}}_2$ groups and water molecules. The energy is found to be lower for a system with a spatially oscillating tilt angle theta than for a flat layer. The cost in free energy of these oscillations is estimated by assuming that where the magnitude of theta is reduced, there is an increase in chain area and hence in chain fluidity. It is found that the free-energy reduction due to the van der Waals interaction is sufficient to compensate for increased chain fluidity at temperatures a few degrees below the chain-melting temperature. Thus the van der Waals energy provides a plausible physical mechanism for the occurrence of the ripple phase. The surface profile predicted is in good agreement with that observed in the $P_{\beta }$ or ripple phase with electron microscopy and characterized by x-ray diffraction. An analytic expression for a negative term in the free energy of the form z’z’’’, where z’=tantheta is derived on the basis of this physical mechanism.

Two diffusive-growth models with an indefinite range of local densities are studied, and their fractal scaling properties are compared with those of diffusion-limited aggregation (DLA). The first model, ‘‘penetrable DLA,’’ differs from standard DLA in that each diffusing particle interacts arbitrarily weakly with an aggregated particle. We derive an analytic expression for the growth rates and find by simulation that the weak interaction leaves the DLA scaling properties unmodified. We explain the observed dependence of the density on the interaction strength. Our second model is a stochastic differential equation, without discrete particles. Simulations of this equation show fractal scaling properties consistent with those of DLA. The scaling of this model shows new subtleties; the average density and the spatial correlations are controlled by different exponents. We describe the reasons for this novel behavior.

We study the problem of velocity and shape selection in the growth of dendritic crystals. We demonstrate that the presence of surface tension destroys the Ivantsov family of solutions at all but a single velocity. This occurs at all undercoolings and for both two-dimensional and axisymmetric three-dimensional dendrites. The lack of a continuous family of solutions is due to a mismatch of terms exponentially small in velocity, in agreement with the mechanism of ‘‘microscopic solvability’’ previously derived for geometrical growth models.

The concept of complete positivity fixes in considerable detail the mathematical structure of quantum Markovian master equations which describe the combined reversible-irreversible dynamics of open systems for the case of time-independent Hamilton operators. For many applications such as, for instance, problems of time-resolved spectroscopy, similar results would be of great value but involve time-varying external fields with a corresponding time-dependent Hamiltonian. For this reason, we propose a suitable extension of the Kossakowski generator to the time-dependent case by maintaining complete positivity and using arguments suggested by experimental facts. As an example, generalized Bloch-like equations can be obtained with three different relaxation times and a nonlinear dependence upon field strength.

A generalized mode-coupling theory of shear and ultrasonic relaxation in viscous supercooled molecular liquids is presented. The theory is based on ideas recently proposed to describe dynamical properties of dense simple liquids and then extended by several authors to discuss the glass transition in such systems. The mode-coupling theory naturally involves a continuum of relaxation times leading to a nonexponential decay of the response to mechanical shear and compressional disturbances. The theory provides a good fit of shear and ultrasound data in supercooled molecular liquids over the entire relaxation region.

Large numbers (hundreds) of quite large [(4–8)×${10}^4$ lattice sites or particles] diffusion-limited-aggregation (DLA) clusters have been grown on two-dimensional square, hexagonal, and triangular lattices to investigate the effects of lattice anisotropy. Similar simulations have been carried out to explore other types of anisotropy, such as anisotropy in the diffusion process and sticking. Our results suggest that the DLA process is sensitive to anisotropy of low symmetry. DLA on the triangular and hexagonal lattices (both with sixfold effective symmetry) lead to structures which can be characterized by a radius of gyration exponent β of 0.585±0.003 (the same as that found for off-lattice DLA). For the square lattice an effective value of about 0.60 is found for the largest cluster sizes used and anisotropy in diffusion or sticking with threefold symmetry leads to even larger radius-of-gyration exponents. Our results suggest that off-lattice DLA and DLA in systems with about fivefold or higher symmetry belong to one universality class and that DLA in environments of lower symmetry lead to structures in a different universality class or classes. Our results for square-lattice DLA are consistent with the theoretical predictions of Turkevich and Sher, but our results for the hexagonal and triangular lattices do not agree with their theoretical prediction. However, in these cases, the discrepancy can be rationalized by using ideas contained in the work of Turkevich and Sher.

The van Hove scattering function S(Q,ω) of liquid sodium has been measured at three states in the temperature range 400 to 800 K for magnitudes of the scattering vector Q between 0.3 and 4.6 A${̊}^{\mathrm{-}1}$. Coherent and incoherent scattering were separated by a model analysis. The incoherent data were analyzed in terms of a collision rate and several shape parameters of $S_s$(Q,ω) such as the reduced half-width γ(Q)=${\omega }_{1/2}$(Q)/(DQ${)}^2$. Results were compared with a kinetic-model theory of Götze and Zippelius, showing good agreement. The observed resonancelike transition of γ(Q) from a diffusive to a more ‘‘hard-sphere-gas’’-like behavior is temperature dependent and indicates no simple relation to the static structure factor of the liquid.

The cooperative diffusion constant of a semidilute polymer solution with a good solvent is studied in the framework of a generalized Kirkwood-Riseman scheme with the aid of a renormalization-group approach. The result agrees well with the recent experimental results due to Wiltzius et al. and Nemoto et al. Why the hydrodynamic screening is unimportant is also discussed.

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

In the past few years a modeling approach has been developed to account self-consistently and simultaneously both for the non-Gaussian and non-Markovian properties of liquids. This uses a nonlinear effective interaction potential between the tagged molecule and a ‘‘virtual’’ Brownian body. The theory describes, in addition, the slope of a correlation function at long times. This is an exponential distinctly slower than that expected from the value of the Debye-type diffusion coefficient. The theory also explains, self-consistently, the slowing down of velocity correlation functions from ensembles of particles whose distribution of equilibrium corresponds to that of an excited state. Previous attempts at disclosing the physical reasons behind these two phenomena have been based on perturbation techniques which can be applied only to a very restricted class of (almost Gaussian and almost Markovian) processes where both the effects are negligible. These limitations are overcome in this paper for distinctly non-Gaussian, non-Markovian processes by using the critically important result that escapes from potential wells are the reasons behind both phenomena. The excited correlation functions are driven by activated rate processes, exhibiting a dependence upon the level of excitation which has recently been recognized to be typical of pumped processes. This would make it possible, in principle, to draw from computer experiments direct information on the nature of the ‘‘virtual’’ potential itself.

A field-theoretic dynamic renormalization-group calculation is carried out to two-loop order for a model of a critical binary liquid undergoing (passive) random stirring. In addition to the mean-field and dynamic ${\phi }^4$ fixed points, a new stable fixed point is found which has a nonanalytic, ${\epsilon }^{1/2}$, ε expansion, where ε≡4-d. The dynamic and static critical exponents for this new fixed point are found to have O(${\epsilon }^{1/2}$) terms. For small stirring Reynolds number, the system will cross over from the dynamic ${\phi }^4$ to the new ${\epsilon }^{1/2}$ fixed point, and we have calculated the effective critical exponents, the static and dynamic correlation function, and the equation of motion, all in crossover form, to one-loop order. The exponent governing the lowering of the critical temperature with stirring Reynolds number is found to be 1.74, which is in agreement with recent experiments of Pine et al. [Phys. Rev. A 29, 308 (1984)].