We perform discrete-mode calculations for a parametric amplifier with a quantum pump and discuss some of the limitations on calculations of this sort in quantum optics. We calculate corrections to the squeezing due to pump quantum fluctuations to order N${¯}^{\mathrm{-}2}$, for a pump initially in a coherent state with average photon number N¯. We find that the limit to the variance of the squeezed quadrature due to the quantum nature of the pump goes as N${¯}^{\mathrm{-}1/2}$. .AE

A three-dimensional quantum theory of stimulated Raman scattering is presented which takes into account a general transverse shape of the pump laser. The transverse spatial autocorrelation function and the intensity of the Stokes pulse are derived analytically, by use of the Maxwell-Bloch equations in low-signal-gain conditions and introduction of a many-spatial-modes approximation. We find that the spatial and temporal coherence are coupled. The transverse coherence depends on the pump-laser shape, and the coherence area increases with increasing gain. Time scales for the buildup of stimulated intensity and correlations for the various transverse parts of the Stokes pulse are obtained.

A new one-dimensional collisionless kinetic model is developed for the flow of ions to probing structures in drifting plasmas. The cross-field flow into the presheath is modeled by accounting consistently for particle exchange between the collection flux tube and the outer plasma. Numerical solutions of the self-consistent plasma-sheath equations are obtained with arbitrary external ion temperature and parallel plasma flow velocity. Results are presented of the spatial dependence of the ion distribution function as well as its moments (density, particle flux, temperature, and power flux). The ion current to the probe is obtained and the ratio of the upstream to downstream currents is found to be well represented by the form R=exp(${\mathrm{Ku}}_d$), where K∼1.7 and $u_d$ is the drift velocity in units of √($T_e$/$m_i$) . The results are in good agreement with comparable recent fluid calculations but show substantial deviations from other models which ignore particle exchange out of the presheath. No evidence is found of the formation of shocks in the downstream wake, contrary to the implications of some fluid theories.

The heating of a plasma by electrons in the simultaneous presence of weak and strong laser fields by the inverse bremsstrahlung process is considered from a quantum-mechanical viewpoint. A kinetic equation is derived and the change in kinetic energy of the plasma electrons is calculated. Results show that the joint action of the two laser beams gives a nonvanishing but large heating rate in the regime of high intensity of the strong field. A physical explanation for this behavior is provided.

With the help of Thomson scattering diagnostics we have measured the density dependence of the He ii $p_{\alpha }$ (468.6 nm) full half-width up to $n_e$=2.2×${10}^{24}$ ${\mathrm{m}}^{\mathrm{-}3}$ and the temperature dependence of the intensity ratio of the C iv (116.9 nm) and C iii (117.6 nm) vacuum-uv lines from 9 to 13 eV. We also present a ready-to-use graphical method for the determination of electron density and temperature from the ion feature of the coherent 90° Thomson scattering (α≫1) from high-density hydrogen plasmas.

We have studied microwave coupling phenomena in linear and nonlinear regimes. Analytic calculations and two-dimensional plasma simulations were carried out for microwave transmission in an apertured coaxial waveguide. In the linear regime, the transmission characteristics for a finite-length aperture that includes the fringing fields were obtained. In the nonlinear regime, where field emission of electrons occurs, we found that the microwave transmission was characterized by the parameter ${\Omega }^2$/${\omega }^2$, where Ω is the electron cyclotron frequency in the electromagnetic field and ω is the microwave frequency. When ${\Omega }^2$/${\omega }^2$≪1 and ${\Omega }^2$/${\omega }^2$≫1, significant microwave power can be transmitted through the aperture. For ${\Omega }^2$/${\omega }^2$≳1, aperture closure due to field-emitted electrons becomes important, and severe degradation of microwave transmission was observed in our simulation.

Flow between two horizontal coaxial cylinders with a partially filled gap is subject to several types of centrifugal instabilities which lead to the formation of a variety of spatial patterns. An experimental investigation has shown that there are five distinct branches of primary instabilities occurring in the system and that four codimension-2 points are easily reached. Theoretical predictions are in qualitative agreement with the observations.

The effective ionization and recombination rate coefficients for Fexvi–Fe xxii were obtained by studying the modulation of line emissions by sawtooth oscillations in the TEXT tokamak. Experimental data are matched with the simulation of iron ion emission by a one-dimensional code. The rate coefficients were determined for $T_e$∼350–900 eV and $N_e$∼(4–5.6)×${10}^{13}$ ${\mathrm{cm}}^{\mathrm{-}3}$. The rate coefficients for Fe xvi, xvii, and xviii have large uncertainty partly due to uncertainty of the temperature profile at large radii of the plasma and partly due to other possible atomic processes. The error of ionization rates for Fe xix–Fe xxii is estimated to be less than 40%, while the estimated accuracy of the recombination rates is better than a factor of 2.

A theoretical formalism and computer code have been developed to calculate spectra of multielectron emitters in plasmas. The plasma electron broadening is treated by a quantum-mechanical relaxation theory. The static-ion approximation is used to treat plasma ion broadening of the atomic levels. Calculated lithiumlike and berylliumlike krypton spectra are compared to experimental spectra obtained in laser implosion experiments at the Laboratory for Laser Energetics, University of Rochester.

The purpose of this paper is to describe a number of theoretical results for fluids consisting of orientationally ordered particles. The model considered assumes perfect orientational order, with all molecules fully aligned in a particular direction with respect to a laboratory fixed frame of reference. However, rotations about the fixed axis are permitted and hence the present theory can be applied to particles which are not axially symmetric. Physically, such a model can represent liquid crystals in a dense nematic phase or fluids of particles aligned by strong electric or magnetic fields. A general formulation is given which allows the hypernetted-chain, Percus-Yevick, and closely related integral-equation approximations to be solved for orientationally ordered systems. For anisotropic fluids it is interesting to analyze the compressibility and pressure tensors and this is done in some detail for particles interacting with both short- and long-range (i.e., dipolar) potentials. The compressibility equation is used to demonstrate microscopically the physical requirement that these tensors be isotropic in a fluid. Also, the conditions placed upon the pair distribution function g(12) by isotropy of the pressure tensor were determined by examining the virial equation of state. For the dipolar case explicit expressions are derived relating the elements of the dielectric tensor to g(12) for an infinite system. Finally, numerical results are presented and discussed for ferrofluids and for another model defined by a closely related but short-range potential.

In diffusive growth models, the local growth rate of a structure is determined by the normal gradient of a diffusive field, with the structure surface an equipotential of that field. The total flux absorbed by the surface varies with the surface position according to a simple formula. This formula can be used to derive scaling laws relating bulk to surface exponents for these models.

We consider physical systems in which microstates can be represented as symbol sequences. The internal correlations in a microstate give restrictions to its ‘‘randomness,’’ quantified by the measure entropy of that microstate. It is shown that, in the thermodynamic limit, the measure entropy for the microstates has an ensemble average equal to the thermodynamic entropy. A simple explanation is that the correlations necessary to generate the whole ensemble can be found in almost any one of its microstates. If microscopic phases are present, there are subensembles, each given by the statistics in almost any one of its microstates. The typical microstate in an equilibrium ensemble can be found by maximization of the measure entropy under energy constraints and general constraints on probability distributions for symbol sequences. The typical microstate does not contain information in correlations of lengths greater than interaction distance, a fact which simplifies the calculation of the entropy for systems with finite interaction length. We exemplify this by deriving the entropy for a monatomic ideal gas and the one-dimensional Ising model with an external field.

Simple models for reaction-limited aggregation (the random addition of pairs of clusters) have been investigated in dimensionalities 2–10 and 20. Simulations have been carried out using both hypercubic lattice models and off-lattice models. For the hierarchical models in which the added clusters are all of the same size, the results are in good agreement with the theoretical ideas of R. C. Ball and T. A. Witten [J. Stat. Phys. 36, 873 (1984)] and of S. P. Obukhov (Zh. Eksp. Teor. Fiz. 87, 2024 (1984) [Sov. Phys.—JETP 60, 1167 (1984)]), which indicate that above a critical dimensionality of $d_c$=2$D^{\mathrm{°}}$ [$D^{\mathrm{°}}$=ln(4)/ln((3/2)] the clusters are mutually transparent and have a fractal dimensionality of $D^{\mathrm{°}}$. Polydisperse models have also been used to investigate both the cluster structure and the kinetics of aggregation. For the case d=2 the mean cluster size (S) and cluster number (N) exhibit an algebraic time dependence and the cluster-size distribution has a peaked form with a cutoff at both large and small cluster sizes. For d>2 the cluster-size distribution can be described quite well by a power-law form with an exponential cutoff at large sizes. For the polydisperse models the simulation results also indicate an upper critical dimensionality for the embedding space or lattice. A polydisperse version of the ‘‘Sutherland’s ghost’’ (transparency) model of Ball and Witten leads to the result $D^{\mathrm{°}}$≃4.0, $d_c$≃8.0, which is consistent with the simulation results. For d<$d_c$ the simulation results are not in good agreement with recent theoretical predictions.

Proton NMR spectra and relaxation times ($T_1$s) at 60 MHz were obtained for the thermotropic compound 4’-n-hexadecyloxy-3’-nitro-biphenylcarboxylic acid, which, upon heating, has the sequence of phases: crystal→${\mathrm{S}}_{\mathrm{C}}$→D (or smectic-D)→${\mathrm{S}}_{\mathrm{A}}$→isotropic. The spectrum narrows over two orders of magnitude upon heating into the D phase, then broadens again in the ${\mathrm{S}}_{\mathrm{A}}$ phase. The spectrum in the D phase is composed of a number of chemical shift peaks, the same as in the isotropic phase, except that the carboxylic acid peak is shifted further downfield in the D phase, evidence of intermolecular hydrogen bonding. In the smectic phases ${\mathrm{S}}_{\mathrm{C}}$ and ${\mathrm{S}}_{\mathrm{A}}$ the spectrum is super-Lorentzian with a width of around 2 kHz, considerably narrowed compared with the 36-kHz-wide spectrum of the solid. The relaxation times increase smoothly from 0.35 s at 124 °C to 0.73 s at 194 °C in the ${\mathrm{S}}_{\mathrm{C}}$ and ${\mathrm{S}}_{\mathrm{A}}$ phases. In the D phase, individual peaks have $T_1$s ranging from 0.18 to 1.1 s, with weighted averages agreeing with the trend of the data from the ${\mathrm{S}}_{\mathrm{C}}$ and ${\mathrm{S}}_{\mathrm{A}}$ phases. Measurements of spin echoes in the D phase without and with a field gradient gave values of about 50 ms for $T_2$ and 3×${10}^{\mathrm{-}11}$ ${\mathrm{m}}^2$/s for the diffusion coefficient. The data indicate that, in the D phase, the molecules sample enough orientations on the time scale of the NMR experiments to average out the dipolar couplings left after the motional narrowing that takes place in the ${\mathrm{S}}_{\mathrm{C}}$ and ${\mathrm{S}}_{\mathrm{A}}$ phases. This is accomplished by diffusion of molecules through regions having different directors.

We present a model to study the heat transfer in the coolant channel of a heat-exchanger system. Such a model introduces thermal fluctuations as well as external noises due to different mechanisms of heat interchange. A unified treatment of both kinds of noise is carried out. The stationary mean value of the channel temperature is studied, obtaining effective transport coefficients which affect the stability of the system. The effects of the different noises are visualized in a correlation length obtained from the temperature correlation function. The model has practical implications in the field of nuclear-reactor noise theory.

For the treatment of inhomogeneous Fermi systems we derive a semiclassical expansion of the linear-response function in powers of ħ (up to ${ħ}^2$) for the interacting (random-phase approximation) and noninteracting (Lindhardt function) case. We find that the series is rapidly converging and that the semiclassical result compares very well with exact model calculations for cases where the response does not exhibit narrow resonances (e.g., the quasielastic peak region); otherwise, it still represents the average value.

The topological properties of cubic structures which have been proposed as models for the cholesteric blue phases (BP) are considered. When the space of the order parameter is restricted to the standard one for biaxial nematics [SO(3)/$D_2$] then, as a consequence of the cubic symmetry, these structures must have disclinations. The usual classification scheme, wherein defect lines are characterized by the conjugacy classes of the fundamental group appropriate to a biaxial system, is used; some exceptions are also noted. For each of the three groups studied [body-centered-cubic $O^5$ (I432) and $O^8$ (I$4_1$32), and simple-cubic $O^2$ (P$4_2$32)] two aspects are considered: general symmetry constraints on disclinations and the topological properties of equilibrium order-parameter distributions as found from Landau-theory calculations. For $O^5$ and $O^2$, there are two nonequivalent symmetry axes upon which there must be disclinations. When they are characterized by a uniaxial order parameter, one must be uniaxial positive and the other uniaxial negative in order for the topology to be consistent with the space-group symmetries. This is not the case for $O^8$ where only one type of defect line, located on the threefold axes, is topologically required. The order-parameter fields obtained from Landau–free-energy minimization have, except in the case of $O^5$, additional disclinations. In particular, the three structures described by the $O^8$ space group are found to have distinctly different networks of defect lines. These, as well as the additional disclination found in the $O^2$ structure, are examined and their group structures were determined. Finally, some open questions and directions for future work are examined.

For the J=0,1 bound states of the muonic ions xyμ (x,y=p,d,t) we calculate the expectation values of the interparticle distances and of the distances squared. We find that the J=1 excited states of tdμ and ddμ are quite large in comparison to all the other states.

Analytically solvable second-order linear differential equations with periodic or quasiperiodic coefficients, common in many areas of physics, are constructed. The equations may contain an arbitrary number of independent parameters. If the equation is interpreted as a Schrödinger equation with a quasiperiodic potential, the solution that is obtained represents an extended wave state. This is the case even if the potential has arbitrarily large positive values.

Closed-form expressions are derived for the finite-mass nonadiabatic corrections to the van der Waals potential in the electric-dipole approximations in terms of London-analog two-center atomic spectral sums. The nonadiabatic corrections to all orders at threshold energy and also those with first-order energy dependence are given.