The theoretical treatment of the optical frequency up-conversion process with stochastic pumping is presented. This process consists of exchange of photons between two modes of different frequencies. It is assumed that the two modes are coupled by a short memory stochastic function. Statistically averaged occupation numbers of both modes were calculated exactly by means of the theory of multiplicative stochastic processes. The obtained nonperturbative solution sums secular terms and is valid for arbitrary times. The oscillatory-damped nature of the exchange of energy between two modes and the role of partial incoherence of the pump is discussed. It is shown that stochastic coupling causes the equipartition of energy between two modes for sufficiently long times. Analogies between an up-converter and a two-level atom driven by a single mode electromagnetic field are indicated. Optical Bloch equations for an up-conversion process are derived.

Contrary to previous reports, the electron scattering cross section of ethene molecules has a Ramsauer-Townsend (RT) minimum at 0.09-0.10 eV. The energy of the RT minimum is much higher than that for nitrogen, slightly lower than that for ethane, and much lower than those for methane and xenon. The scattering of low-energy (${10}^{-3\mathrm{}}$-1 eV) electrons by nonpolar molecules in the low-density gas phase is strongly influenced by the molecular shape. The mobility of electrons (the proportionate rate of motion in the direction of an applied electric field) in the low-density gas is mainly governed by elastic collisions, but the removal of energy gained from the field occurs mainly through inelastic collisions. The latter must involve predominantly molecular rotational transitions at the energies involved (<0.1 eV). In the dense gas at $\frac{n}{n_c}\gtrsim 0.2$ the density-normalized mobility $\mu n$ decreases due to electron quasilocalization and transient-anion formation. The transient anions in ethene are much more ephemeral than those formed in dense nitrogen vapor. The anion state becomes less ephemeral with increasing density and decreasing temperature in the liquid phase.

We consider a ring of tightly torsion-coupled, overdamped pendulums subject to an external torque and coupled to a thermal reservoir. At low temperatures the dynamics of this system, over a wide range of forces, is governed by thermally activated kink-antikink pairs, their subsequent separation through the external force, and eventual recombination by collision with other kinks. We calculate the thermal activation rate of kink-antikink pairs using an approach first developed by Brinkman. This theory requires a detailed investigation of the multidimensional saddle, which has to be crossed, if the system is to make a thermally activated transition. The propagation velocity of the driven kinks is calculated. We use these results to derive the mean angular pendulum velocity as a function of the applied torque. Comparison is made with earlier work.

The pressure of a classical simple fluid of particles interacting with square-well potentials is computed by a method combining the use of a parametric integral equation with first-order perturbation theory. This method leads to a simple expression for the pressure of the fluid. In contrast to the usual choice, the reference part of the potential energy is taken to be a square well itself. The results are in good agreement with pressure values from molecular dynamics and are relatively insensitive to the choice of the reference-well depth, provided that that well is shallow. Based on these findings, fine-meshed tables giving (reduced) pressure, internal energy, and Helmholtz free energy are constructed for ranges in reduced density and temperature of $n^{*}\le 0.85$, $1.4\le T^{*}\le 4.0$. These tables should provide reliable estimates of the thermodynamic variables for a square-well gas at any ($n^{*}$, $T^{*}$) within the given ranges; they also help to lay the basis for comparative studies of the applicability of perturbation theory to the square-well gas.

We study chaotic systems generated by deterministic or probablistic mappings. We introduce the density function which is an eigenfunction of a probability-preserving kernel $K$. We are able to show that all eigenvalues of $K$ have magnitude less than or equal to 1 and that the only magnitude-one eigenvalues are the $N\mathrm{th}$ roots of unity. We have also calculated the corresponding eigenfunctions associated with these magnitude-one eigenvalues: These eigenfunctions can be expanded in terms of $N$ positive functions having disjoint support. We then concentrate on a one-dimensional system, and study the behavior and mechanism for various chaotic transitions. We find that the mechanism associated with the 2 to 1 (or more generally, $2N$ to $N$) transition is different from those associated with other chaotic transitions. We then determine the conditions for these transitions, and express them in a universal form. We confirm the Huberman-Rudnick scaling in the large $2^n$ to $2^{n-1\mathrm{}}$ chaotic-transition region, and determine the prefactor at these transitions. In addition, we establish a simple relation between the Lyapunov exponent and the folding of the distribution functions. We have also studied the chaotic regions of this system numerically.

Dielectric relaxation studies in nematic mixtures of $p$-pentyl-$p^{\prime }$-cyanonobiphenyl and $p$-pentyl-$p^{\prime }$-cyanoterphenyl show two relaxation processes with different activation energies for $\overrightarrow{\mathrm{E}}\parallel \overrightarrow{\mathrm{n}}$. Dielectric relaxation with $\overrightarrow{\mathrm{E}}\parallel \overrightarrow{\mathrm{n}}$ is predominantly a single-particle process and probes molecular interactions at large angles.

The relative intensities of the $2l2l^{\prime }$ dielectronic satellite transitions of C v have been measured as functions of electron density and temperature in a laser-produced plasma. The relative intensity of the $2p^2{}_{}{}^3{}_{}{}^{}P-1s2p{}_{}{}^3{}_{}{}^{}P$ transition is observed to vary with electron density in the range 8×${10}^{19}$ to 2×${10}^{20}$ ${\mathrm{cm}}^{-3\mathrm{}}$. In this density range, the satellite line intensities are consistent with electron collisional population of the $2p^2{}_{}{}^3{}_{}{}^{}P$ level from the $2s2p{}_{}{}^3{}_{}{}^{}P$ level, both doubly excited. The measured rate coefficient for this collisional transition, inferred from the density dependence of the $2p^2{}_{}{}^3{}_{}{}^{}P$ spectral radiation, agrees with recently calculated values. In contrast to previous higher-$Z$ experiments, electron collisional population of the $2p^2{}_{}{}^3{}_{}{}^{}P$ level from the singly excited $1s2p{}_{}{}^3{}_{}{}^{}P$ level is found to be unimportant in this experiment.

The Langevin formalism that describes fluctuations about thermodynamic equilibrium is extended to study hydrodynamic nonequilibrium steady states. The limitations of our generalization are discussed as well as the connection between experimental and theoretical quantities which is more subtle than in equilibrium. The spectrum for Brillouin scattering from a fluid in a shear flow or temperature gradient is simply obtained by Langevin methods. The latter problem exhibits an asymmetry in the height of the peaks inversely proportional to the square of the scattering wave vector. We also construct a microscopic ensemble that is applicable to a variety of hydrodynamic nonequilibrium steady states, and then verify for a particular model that our extension of the Langevin method agrees with a fully microscopic calculation.

A microwave-afterglow mass-spectrometer apparatus has been used to determine the dependence on electron temperature $T_e$ of the recombination coefficients ${\alpha }_n$ of the dimer and trimer ions of the series $\mathrm{C}{\mathrm{O}}^{+}·{\left(\mathrm{CO}\right)}_n$. We find ${\alpha }_1=(1.3\mathrm{}\pm 0.3)\times {10}^{-6\mathrm{}}{\left[\frac{T_e\left(\mathrm{K}\right)}{300}\right]}^{-0.34\mathrm{}}$ and ${\alpha }_2=(1.9\mathrm{}\pm 0.4)\times {10}^{-6\mathrm{}}{\left[\frac{T_e\left(\mathrm{K}\right)}{300}\right]}^{-0.33\mathrm{}}$ ${\mathrm{cm}}^3$/sec. These dependences on $T_e$ are quite different from those obtained previously for polar-cluster ions of the hydronium and ammonium series but are similar to that for simple diatomic ions.

A dynamic renormalization-group method is developed to study the ultraviolet properties of velocity correlations generated by the Navier-Stokes equation with a random stirring force with the correlator decreasing as $k^{-y}(y\ge d)$ at $k\to \infty$. It is shown that the elimination of modes from a shell near the infrared cut-off $k_0\approx \frac{1}{L}\to 0$ results in two major effects: transition to a frame of reference moving with random velocity ${\overrightarrow{\mathrm{v}}}_L$ ($c_L^{2}a{L}^{\frac{2}{3}}$ if $y=d$) and the appearance of a negative dissipation in the Navier-Stokes equation proportional to $k^{\frac{2}{3}}$. All the divergent terms are summed up into a kinematic effect of a transfer of small eddies by large ones and the dynamics is determined by convergent series. Long-time, large-scale behavior of a fluid is identical with the one obtained by Martin and de Dominicis, Lucke, and Fournier and Frisch. It is shown that the theory is asymptotically free in the ultraviolet region for any $\epsilon =d-y\le 0$. The energy spectrum of a stirred fluid is $E\left(k\right)\mathrm{}a\left[\frac{k^{-\frac{5}{3}}}{\ln \mathrm{}\left(\mathrm{kL}\right)\mathrm{}}\right]$ for ($d=y$) and the Kolmogorov spectrum without corrections never exists in the ultraviolet limit.

In this paper we consider the problem of computing the quantum-mechanical corrections to the thermodynamic properties of systems whose two-particle interaction may be described by a Lennard-Jones 6-12 potential. Using a procedure first developed by Feynman, together with physical arguments, we develop an effective two-particle 6-12 potential which includes quantum-mechanical corrections. Using this potential in conjunction with the theory of corresponding states we compute the quantum effects on: (i) the second virial coefficient, (ii) the critical-point location, (iii) the surface tension, (iv) the critical-point amplitudes and exponents, (v) the correction to scaling amplitudes and exponents, (vi) the liquid-gas and solid-liquid phase boundaries, and (vii) the Debye temperature at the melting point. In all cases there is good qualitative and frequently quantitative agreement with experimental results. The theory is limited to "high temperatures" since exchange effects are not included.

The frequency dependence of diffusion in a classical fluid is a consequence of the frequency dependence of the viscosity and leads to a small but observable deviation from a pure exponential decay of the order-parameter fluctuations. Our calculation of the deviation at the critical point gives a good fit to the data of Burstyn, Chang, and Sengers. The theory also agrees with the temperature dependence that they found.

The scaling hypothesis is now widely used in polymer statistics because of the correspondence between this problem and the $n\to 0$ limit of the $n$-vector model of magnetism. We prove here that if the $n\to 0$ vector model satisfies scaling, then its free energy does not always satisfy the usual convexity requirements of thermodynamic stability, even above the critical temperature in small fields. We also show that, because of the very different role played by the field variables in the two interpretations, the corresponding model of polymer solutions does not suffer from this instability.

The temporal evolutions of structure functions $S_k\mathrm{}\left(t\right)\mathrm{}$ of quenched binary mixtures are studied theoretically. With the aid of a Langevin-type equation, basic nonlinear kinetic equations for the composition fluctuation are derived for a purely dissipative system and for a fluid mixture. Predicting that the free energy is expanded on the basis of a cluster gas picture, the equations of motion for structure functions are derived. The inverse nonhydrodynamic susceptibility ${{\chi }_k}^{-1\mathrm{}}$, which is the first-derivative coefficient of the free energy, and $S_k\mathrm{}\left(t\right)\mathrm{}$ are assumed to have the form $R^{-d}\tilde{\chi }{\mathrm{}\left(\mathrm{kR}\right)\mathrm{}}^{-1\mathrm{}}$ and $R^d\tilde{S}\mathrm{}\left(\mathrm{kR}\right)\mathrm{}$ in $d$ dimensions. Here $R$ is the average cluster diameter, which behaves as $t^{-a^{\prime }}$ [$a^{\prime }={\mathrm{}(d+2\mathrm{})\mathrm{}}^{-1\mathrm{}}or{\mathrm{}(d+3\mathrm{})\mathrm{}}^{-1\mathrm{}}$ for a purely dissipative system and $a^{\prime }=\frac{l}{d}$ for a fluid mixture]. If ${{\chi }_k}^{-1\mathrm{}}$ has a gap of the order $R^{-d}$, then our calculation of $S_k\mathrm{}\left(t\right)\mathrm{}$ yields good agreements with experiments (for $d=3\mathrm{}$). The renormalizations both the mobility and of susceptibility due to long-range hydrodynamic interactions are treated with the use of the mode-coupling technique.

We generalize the familiar result that the drift velocity $V_d$ and the product $\mathrm{pD}$ of the pressure and the diffusion coefficient depend on pressure $p$ and electric field $E$ only through the ratio $\frac{E}{p}$ in swarm experiments. Our new scaling law applies to different systems to the extent that their elastic and inelastic cross sections are in the same ratio. We present model calculations of $V_d$ for electrons in gaseous C${\mathrm{H}}_4$-Ar and C${\mathrm{H}}_4$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixtures predicting that the scaling is approximately obeyed if the C${\mathrm{H}}_4$ concentrations are appropriately related. We also examine $V_d$ and $D_{\perp }$ data for electrons in C${\mathrm{H}}_4$ and Si${\mathrm{H}}_4$ at low $E$ and find that the scaling is approximately obeyed with a factor of 6. This suggests strongly that the low energy (≲1 eV) effective elastic and inelastic electron cross sections for these molecules have approximately the same shape and differ by the same factor, which is approximately 6. Thus in particular we predict a Ramsauer minimum for Si${\mathrm{H}}_4$, which has been suggested previously.

The drift of electrons in mixtures of methane with argon and helium is measured with a double shutter drift tube as a function of methane composition and electric field-pressure ratio $\frac{E}{p}$. At certain concentrations, inelastic scattering by methane causes a maximum in the drift velocity as a function of $\frac{E}{p}$. As the methane mole fraction decreases, the drift velocity maximum decreases and moves to lower values of $\frac{E}{p}$. In the argon mixtures, the drift velocity at low $\frac{E}{p}$ is greater than it is in either pure gas. Comparision is made with direct numerical solutions of the Boltzmann equation for the mixtures. When the methane mole fractions are appropriately chosen, the data obey roughly a scaling law relating the electron drift velocity versus $\frac{E}{p}$ in a methane-argon mixture with $V_D$ versus $\frac{E}{p}$ in a methane-helium mixture.

New Hartree-Fock (HF) solutions are presented for a one-dimensional gas with attractive delta-function interactions. They are found by recourse to the variational principle and have, as special limiting cases, both the exact, zero-density HF solution and the plane-wave orbitals.