We show that the most complete and accurate description of fluctuations in quantum-optical systems is that obtained using the generalized Wigner distribution for the macroscopic observables of the system. The smallness of the inverse of the saturation photon number entitles us to neglect the terms with derivatives of order higher than second order in the time-evolution equation for the quasiprobability distribution. This treatment allows us to also describe correctly nonclassical effects such as photon antibunching or "squeezing," which are maltreated or even destroyed if one neglects the atom-atom correlations. We derive and analyze the Fokker-Planck equation for the Wigner function in the case of the usual laser and compare the results with those following from other approaches. In the region very high above threshold we find a small antibunching effect, which was not discovered in previous treatments due to the neglect of atom-atom correlations.

Wavelengths and atomic parameters for both dielectronic and inner-shell satellite lines of the type $1s^{2}nl-1s2\mathrm{}{l}^{\prime }n{l}^{\prime \prime }$, with $n=2, 3, \mathrm{and} 4$, have been calculated for ${\mathrm{Ti}}^{19+}$. The atomic data were calculated in a multiconfiguration intermediate-coupling scheme and are compared with previous results for $n=2\mathrm{}$. The intensities of the higher-$n$ satellites are derived from these data and thus an estimate of the contribution of the unresolved dielectronic satellites to the resonance line is obtained. Direct excitation rates are also given for the resonance, intercombination, and forbidden lines for He-like titanium. Cascades and the effect of resonances for these lines are not considered in this paper. These results are used to fit an experimental soft-x-ray spectrum from the Poloidal Divertor Experiment tokamak discharge. Good agreement is obtained between computed and observed spectra.

Two-dimensional Fourier transforms of convection patterns are computed from data obtained by Doppler scanning of the velocity field. This new technique is used to study the time dependence of the wave-number distribution, and the variation of the mean wave number $k^{*}$ with Rayleigh number $R$. We find that $k^{*}$ increases by about 15% during the pattern evolution following a step change in $R$ from below $R_c$ to $2R_c$. This increase is associated with a reduction in the number of defects in the pattern. The dependence of $k^{*}$ on $R$ is characterized by a decline above $R_c$ and a steeper decline near $5R_c$ where the skewed varicose instability causes the flow to become time dependent. The peak in the wave-number distribution does not shift significantly in the range $6-40R_c$, and still contains about half of the spectral power at $40R_c$. The flow apparently remains largely two dimensional.

Measurements of the quasielastic spectra have been made with a three-axis neutron spectrometer at constant-$Q$ mode in a temperature range from 38°C down to -20°C. Two energy resolutions both high ($\Delta E=100\mathrm{}$ μeV) and low ($\Delta E=800\mathrm{}$ μeV) were used to identify and separate a sharp component from a broad one. As temperature is decreased below zero the spectrum shows an increasing sharp component standing out on top of the broad one. The broad component is attributed to rotational motions of water molecules. A preliminary analysis of the linewidths gives a $Q$-independent relaxation time which has the same magnitude as the rotational relaxation time measured by nuclear magnetic resonance. The $Q$ dependence of the sharp line is analyzed by a $Q$-dependent diffusion coefficient. A temperature-independent characteristic length $l_0=0.5\mathrm{}$ Å is obtained. We then attempt to relate this length to local geometry of protons associated with hydrogen bonding.

An experimental study of the chaotic states and the routes to chaos in the driven pendulum as simulated by a phase-locked-loop electronic circuit is presented. For a particular value of the quality factor ($Q=4\mathrm{}$), for which the chaotic behavior is found to be rich in structure, the state diagram (phase locked or unlocked) is established as a function of driving frequency and amplitude, and the nature of the chaos in these states is investigated and discussed in light of recent models of chaos in dynamical systems. The driven pendulum is found to exhibit symmetry breaking as a precursor to the period-doubling route for chaos. Although period doubling is found to be fairly common in the phase-locked states of the pendulum, it does not always manifest itself in complete bifurcation cascades. Intermittent behavior between two unstable phase-locked states is also commonly observed.

A numerical experiment is conducted on the decay of a sine-Gordon breather under simple dissipation. Both the spatial configuration and the (nonlinear) spectral configurations are measured numerically. The spectral configuration establishes that the breather is annihilated in finite time and that the annihilation process is accomplished by the generation of a long-wavelength packet of dispersive radiation. The nonlinear radiation density, which is measured numerically, is seen to be order 1 and is extremely well approximated by a sech profile in $k$ space. Finally, a representation of the spectral configuration by "resonance" states is investigated.

A time-dependent projection-operator formalism is used to derive a kinetic equation for the single-spin density operator in an Ising system of $N$ two-state spins in weak interaction with a heat bath. This equation contains a contribution at the self-consistent-field level and also higher-order contributions due to dynamically generated correlations. A detailed evaluation of the self-consistent-field terms is made. Possibilities for generalizing the method to obtain equations for multispin density operators are discussed.

We consider the steady flow of $K$ interacting currents through a uniform barrier composed of material satisfying a linear flow equation $J_m={\gamma }_{\mathrm{mn}}\left(\beta \right)\left(\frac{d{\beta }_n}{\mathrm{dx}}\right)$. ${\beta }_k$ is the affinity associated with the current $J_k$. Using nonlinear reciprocity relations previously derived from microscopic time reversibility we derive a set of nonlinear constraints involving the derivatives of the conductivity matrix ${\gamma }_{\mathrm{ij}}$ with respect to the affinities ${\beta }_1,\dots ,{\beta }_K$. The constraints are verified with the use of a model of ideal-gas flow through a porous plug.

An extension of the Peierls argument due to Heilmann is used to prove the existence of an ordered phase in two lattice-gas models of orientable molecules. The first model is a lattice gas of tetrahedral molecules on a body-centered-cubic lattice. The second model is a lattice gas of trigonal planar molecules on a triangular lattice. A lattice site in either model can be vacant or occupied by a molecule in either of the two orientations in which the molecular bonds point toward neighboring lattice sites. Two neighboring molecules attract if one points a bond toward the other and repel if both molecules point bonds toward one another. The ordered phase in the three-dimensional model has the same orientational ordering that has been proposed to exist in liquid carbon tetrachloride. The ordered phase in the two-dimensional version has the structure indicated by Monte Carlo studies to exist in a system of methane adsorbed on graphite.

The drumhead model describing the interface separating two coexisting phases is analyzed on a lattice. A strong-coupling transformation allows asymptotic results for the interface fluctuations in the limit of weak pinning to be extracted. The model exhibits roughness for bulk $d\le 3$. An exact solution for the free energy in bulk $d=2\mathrm{}$ has been obtained. Comparison with work of Buff, Lovett, and Stillinger and of Wallace and Zia is made.

We study the connections between the chain summations of variational theories of Fermi fluids and those generated by ring-diagram summations in the correlated-basis-functions (CBF) perturbation theory. The effective interactions of CBF theory and the random-phase-approximation (RPA) equations in the correlated basis are rewritten in an irreducible form. We discuss local approximations to the irreducible vertex which are sympathetic with the use of variational wave functions. They allow contact to be made with conventional formulations of the RPA, to weak-coupling, pseudopotential, or "local-screening" theories. Our studies lead also to consistency requirements between variational calculations of ground-state properties and the effective interactions used in CBF theory.

Fractal properties of a random pattern formation produced by computer simulation have been analyzed. The controlling parameter was a tip priority factor $R$ by which a growing tip grows further compared to any site on a branch to produce a new side branch. The pattern was found to show an approximate self-similarity and associated with two fractal dimensions: One is the inner dimension which measures the fine structure and the other is the outer dimension which measures the framework of the pattern. With increasing tip priority factor, the inner dimension decreases and shows a phase-transition-like behavior at $R=35\mathrm{}$. It shows damped oscillations approaching a constant value as the volume is increased. The outer dimension roughly remains 2. A possible mechanism for these behaviors is discussed.

The simulated time evolution of magnetic-field profiles and trapped flux in a field-reversed configuration, when compared with the experiment, implies that the rapid decay of the initial reversed flux is due to a resistivity that is anomalously enhanced over its classical value. A tenuous plasma between the field-reversed configuration and the wall carries a significant fraction of the current, and about half of the anomalous Joule heating must be deposited directly in the ions in order to calculate the correct ion temperature. The fractional flux retention is most sensitive to an increase of applied bias field.

A theoretical analysis based on the concepts and techniques of statistical physics is carried out for two nonlinear models of diffusion of information—one in a closed population and the other in an open one. Owing to interpersonal contacts among the members of the population, the models exhibit a cooperative behavior when a certain parameter of the problem approaches a critical value. Mathematical similarities in the behavior of the two models, in the vicinity of the critical point, are so impelling that one is tempted to investigate the corresponding behavior of a generalized model, which can be done by carrying out a systematic system-size expansion of the master equation of the process and thereby deriving a nonlinear Fokker-Planck equation for the relevant probability distribution. This establishes a broader class of systems displaying identical behavior in the critical region and also elucidates the role played by fluctuations in bringing about the cooperative phenomenon.

Based on the well-known low-density expansion for the ground-state energy per particle of a many-fermion system interacting pairwise via a central potential we develop a perturbation scheme in which the zero-order state is that of the purely-repulsive-spheres fluid. For the hard-core plus square-well pair-interaction case we have deduced, for two-species fermion matter, perturbation formulas up to sixth order in the attractive coupling parameter. We explicitly report results up to fourth order here. Padé-approximant analyses in the density are carried out in each order with the intent of providing the basis necessary for extensive equation-of-state calculations of various many-fermion systems. In particular, for zero order (the fermion hard-sphere fluid) we predict an uncertainty-principle divergence in the energy, and hence pressure, corresponding to the random close packing of spheres, at a density of about 0.5 times the recently obtained value for boson hard spheres and about 0.2 times the well-known empirical value for classical hard spheres.

The amplitudes of the correlation length (${\xi }_0^{+}$,${\xi }_0^{-}$) and (${\xi }_0^c$) on the critical isotherm, the susceptibility ($C^{+}$,$C^{-}$) and ($D$) on the critical isotherm, the order parameter ($B$), and the specific heat ($A^{+}$,$A^{-}$), have been obtained for eight binary fluids in the homogeneous (+) or the heterogeneous region (-). All the values have been inferred using the universal values of critical exponents. An accurate approximation for the correlation function, which however does not include corrections to scaling, has been used to deduce ${\xi }_0^{+}$ and $C^{+}$ from light scattering measurements. Spectral analysis of the scattered light allows absolute values of $C^{+}$ to be obtained from the Rayleigh-Brillouin ratio without any assumptions concerning the Reyleigh factor expression. The critical anomaly of the refractive index has been used in several cases to estimate the specific-heat anomaly. Values have been obtained for height amplitude combinations, $\frac{A^{+}}{A^{-}}$, $\frac{C^{+}}{C^{-}}$, $\frac{{\xi }_0^{+}}{{\xi }_0^{-}}$, $R_c^{+}=\frac{A^{+}{C}^{+}}{B^2}$, $R_{\chi }^{+}=C^{+}D{B}^{\delta -1\mathrm{}}$, $R_{\xi }^{+}={\xi }_0^{+}{\left(A^{+}\right)}^{\frac{1}{3}}$, $R_{\xi }^{+}{\left(R_c^{+}\right)}^{-\frac{1}{3}}={\xi }_0^{+}{\left(\frac{B^2}{C^{+}}\right)}^{\frac{1}{3}}$, and $Q_2=\left(\frac{C^{+}}{C_c}\right)\left(\frac{{\xi }_0^c}{{\xi }_0^{+}}\right)$. The universality of these ratios is well supported, and the values found are in agreement with those given by the high-temperature series and the renormalization-group approaches. The experimental values of $\frac{C^{+}}{C^{-}}$ and $R_{\xi }^{+}$ are found to be closer to the renormalization-group prediction.

The fluorescence temporal profiles for donor and acceptor molecules in the binary mixtures of (1) rhodamine $6G$ and oxazine-4-perchlorate and (2) rhodamine $B$ and nile-blue-$A$-perchlorate were measured using a 6-ps laser pulse and streak camera-video system. The theoretical calculations were fitted to the experimental data to obtain fundamental information concerning energy-transfer dynamics in binary mixtures.

An equation of state for $D$-dimensional $\nu$-component classical plasmas that interpolates very effectively between the "Debye-Huckle" and "ion-sphere" limits is derived. Extensive analysis for three-dimensional ($D=3\mathrm{}$) two-component ($\nu =2\mathrm{}$) plasmas is presented.

A new method presented here for calculating the equation of state for classical systems is very fast, employs the same algorithm for all solid and fluid densities and temperatures, and is of accuracy comparable with that of the computer simulations. The method consists of fitting the pair potential by a linear combination of potentials belonging to a basis set (for which the inverse power potentials are a good choice) and of employing a property of additivity of equations of state when these are considered in terms of the density and excess entropy as the independent variables. The new method accomodates the static lattice sum, or any physical quantity that is expected to be additive in pair-potential contributions, as naturally as the pair potential itself, and should be very useful in the study of equations of state for real materials. There are indications for the validity of the new method in two dimensions as well.

We show that with suitable assumptions the equilibrium states are exactly the states invariant under adiabatic local perturbations. The relevance of this fact to the problem of ergodicity is discussed.