The ground-state energy of the Hamiltonian $-\left(\frac{1}{2}\right)\frac{d^2}{d{x}^2}+\lambda V\left(x\right)\mathrm{}$ is analyzed in terms of the zeros of a perturbative expansion for the inverse of the $T$ matrix, and an expression for ${\mathrm{}(-2E)\mathrm{}}^{\frac{1}{2}}$ correct to order ${\lambda }^4$ is obtained. Modifications of the results for long-range potentials of the type $V\left(x\right)\mathrm{}\to -a_{\pm }{\mathrm{}\left|x\right|\mathrm{}}^{-n}$, $n=1,\dots ,4\mathrm{}$ at $x\to \pm \infty$ are discussed. The problem of three-body bound states is considered, leading to an expression for the ground-state energy of He-like atoms with nuclear charge $\alpha \gg 1$, in a strong magnetic field.

On the basis of the absorptive bistability model, including the fluctuations, we rederive in the good-cavity limit the Fokker-Planck equation describing the time evolution of the quasiprobability distribution for the transmitted field amplitude. It is shown that on a semiclassical level different variants of the Fokker-Planck equation are possible. The equation of Bonifacio, Gronchi, and Lugiato is solved in terms of a path integral which involves a generalized Wiener measure. In order to calculate the averages of transmitted field moments as functions of time, a Monte Carlo integration scheme is used. This scheme consists in constructing random trajectories which result from the Langevin equation statistically equivalent to the derived Fokker-Planck equation. Numerical results in the bistable domain are presented for large values of the fluctuation parameter.

A nonlinear interferometer driven with a partially coherent light field is analyzed. A limit on the fluctuations permissible in the driving field to observe bistability is calculated. For a Gaussian, broadband input field the transmitted radiation is shown to have enhanced intensity fluctuations.

This paper presents a generalization of the theory of geometric optics in plasmas where the local dielectric tensor $\epsilon (\overrightarrow{\mathrm{k}},\omega ;\overrightarrow{\mathrm{r}},t)$ is not almost Hermitian, as heretofore assumed. It is shown that for general $\epsilon$ one can construct the formalism so that the new theory is characterized by the same equations determining the rays, and the equation for the amplitude of the wave along the rays is unmodified in structure. The theory uses the quasidispersion relation $\det \left\{\epsilon \right(\overrightarrow{\mathrm{k}},\omega +i\nu ;\overrightarrow{\mathrm{r}},t\left)·{\left[\epsilon \right(\overrightarrow{\mathrm{k}},\omega -i\nu ;\overrightarrow{\mathrm{r}},t\left)\right]}^{*}\right\}=0\mathrm{}$ to find the complex roots $\omega +i\nu$, where when the approximation of short wavelength compared with the scale length underlying geometric optics holds, the real part $\omega$ serves to generate the rays via $\overrightarrow{\mathrm{r}}={\omega }_{\overrightarrow{\mathrm{k}}}$, and the imaginary part $\mathrm{iv}$ enters the transport equation for the amplitude.

The generalized Enskog model solution of Furtado et al. for the Brillouin spectrum $S(q,\omega )$ is compared with the experimental results for compressed He, Ne, and Ar. A discrepancy between the two which localizes around the Brillouin component at high densities is found. It is also noted that the calculated spectrum disagrees with the equivalent curve for pure hydrodynamics at high densities and with an equivalent-model solution of the Boltzmann equation at low densities.

A new Hamiltonian method for deformation simulations is related to the Green-Kubo fluctuation theory through perturbation theory and linear-response theory. Numerical results for the bulk and shear viscosity coefficients are compared to corresponding Green-Kubo calculations. Both viscosity coefficients depend similarly on frequency, in a way consistent with enhanced "long-time tails."

We have studied by inelastic coherent thermal-neutron scattering the many-body effects introduced into a fluid by the presence of a light nearly invisible second component. We have observed this effect over a range of wave vectors and frequencies from where the effect is pronounced to where it is no longer experimentally observable.

We have made Monte Carlo calculations of the pair correlation function $g\left(r\right)\mathrm{}$ of a dense gas along the 297 K isotherm using a published pair potential for krypton. Eleven states were simulated, and then, using the pair potential plus the Axilrod-Teller triple-dipole potential, seven states were simulated. The effect of the triplet potential was very small except near the principal peak of $g\left(r\right)\mathrm{}$. We compare, in real and Fourier space, these results to the virial expansion of $g\left(r\right)\mathrm{}$ at low densities to test its range of validity. This work provided the background for the interpretation of the experimental data of Teitsma and Egelstaff on real krypton gas, and examples are given involving the extraction of the pair- and triplet-potential terms.

We study by computer simulation the behavior at low energy of two-dimensional Lennard-Jones systems, with square or triangular cells and a number of degrees of freedom $N$ up to 128. These systems exhibit a transition from ordered to stochastic motions, passing through a region of intermediate behavior. We thus find two stochasticity borders, which separate in the phase space the ordered, intermediate, and stochastic regions. The corresponding energy thresholds have been determined as functions of the frequency $\omega$ of the initially excited normal modes; they generally increase with $\omega$ and appear to be independent of $N$. Their values agree with those found by other authors for one-dimensional LJ systems. We computed also the maximal Lyapunov characteristic exponent ${\chi }^{*}$ of our systems, which is a typical measure of stochasticity; this analysis shows that even in the ordered region certain stochastic features may persist. At higher energies, ${\chi }^{*}$ increases linearly with the energy per degree of freedom $e$. The law ${\chi }^{*}\mathrm{}\left(e\right)\mathrm{}$ has been determined in the thermodynamic limit by extrapolation. The values found for the stochasticity thresholds fall in a physically significant energy range. The behavior of the thresholds as a function of $\omega$ and $N$ is compatible with the hypothesis on the existence of a classical zero-point energy, advanced by Cercignani, Galgani, and Scotti.

A quantum-statistical-mechanical theory of nonequilibrium stationary states (NESS) is presented. The average of an arbitrary dynamical operator is calculated. The theory is applied to correlation functions in a heat-conducting NESS of the Heisenberg ferromagnet. Significant changes (as compared with equilibrium) are found. Correlation functions that vanish in equilibrium due to symmetry are allowed and are very important for $\overrightarrow{\mathrm{k}}$ vectors in the hydrodynamic regime. In the absence of magnetic field, the change with respect to equilibrium is pronounced. A static correlation that depends on $k$ as $\frac{1}{k^7}$ is found. Such correlations are expected to be seen experimentally when magnon-phonon interactions can be neglected (i.e., $k>\mathrm{}{10}^6$ ${\mathrm{cm}}^{-1\mathrm{}}$). The influence on time correlation functions is examined and found to be well within experimental detectability.

The two-dimensional ($2D$) crystal and the $3D$ smectic-$A$ liquid crystal are examples of Landau-Peierls systems, where long-wavelength fluctuations wash out long-range order of the order parameter. However, the decay of the order-parameter correlation functions is of the power-law type, rather than exponential. The result is that in x-ray scattering characteristic power-law singularities appear instead of the usual Bragg peaks. The details of these singularities, which have recently been observed experimentally in a smectic-$A$ liquid crystal by Als-Nielsen et al., are analyzed for the smectic-$A$ case. A new scaling property of the structure factor is derived as a function of the momentum-transfer components parallel ($\kappa$) and perpendicular ($K_{\perp }$) to the smectic layers. Very close to the Bragg points, finite-size effects become important, including a new and unusual effect when $K_{\perp }$ is proportional to the inverse square root of the finite thickness of the specimen. The crossover in the Bragg peaks due to order-restoring effects of an external magnetic field is presented.

The cycle that maximizes the average power output of a class of irreversible heat engines has been obtained using optimal control theory. This class of heat engines is distinguished by being endoreversible, having a fixed compression ratio and being irreversible because of linear heat conduction. The optimal cycle is found to have eight branches including two fixed-volume branches, two isothermal branches, and two maximum-power branches. Maximum-power branches are defined and discussed in detail. It is shown that the maximum-power cycle contains no adiabatic branches. Two special limits are analyzed in detail, the Curzon-Ahlborn limit and the large-compression-ratio limit. The fixed-compression-ratio constraint and the periodicity of the engine require special attention which lends this problem some purely mathematical interest.

Integral $K$-shell Compton-scattering cross sections in elements Fe, Ni, Cu, Zn, As, Se, and Br have been determined for 279-keV photons. The results when compared with theory suggest that $K$-shell electrons in the elements under investigation behave as free electrons.

Huang and Hughes have recently discussed the hyperfine splitting $\Delta \nu$ of muonic helium (${\alpha }^{++}{\mu }^{-}{e}^{-}$) using a variational approach. In this paper, the Born-Oppenheimer approximation is used to simplify the evaluation of $\Delta \nu$ in the nonrelativistic limit. The first-order perturbed wave function of the electron is obtained in closed form by slightly modifying the method used by Dalgarno and Lynn. The result $\Delta \nu =4450\mathrm{}$ MHz, is quite close to the published result of Huang and Hughes 4455.2±1 MHz, which required a very large Hylleraas expansion as well as considerable extrapolation.

Measurements of the incident-ion energy dependence of $L\alpha -\mathrm{t}\mathrm{o}-\mathrm{Ll}$ x-ray intensity ratios are reported for protons incident at 0.40 to 2.20 MeV/amu on thin targets of Pb and for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and C ions incident upon Yb. The data are compared to calculations of the $L\alpha -\mathrm{t}\mathrm{o}-\mathrm{Ll}$ ratio which include the effects of alignment of the $2p_{\frac{3}{2}}$ state of the target.

The recent prediction of ${\mathrm{H}}^{-}$ photodetachment peaking orthogonally to the light polarization, and the underlying considerations of SO(4) symmetry by Herrick are illustrated in terms of vector diagrams. We emphasize the role of the helicity of the SO(4) operators $\overrightarrow{1}\pm \overrightarrow{b}$, a phenomenon that is also apparent in the construction of the fundamental "spinor" representation of the Lorentz group and in the emerging of electron spin from the Dirac theory.

The theoretically derived $\alpha$ values in the $X\alpha$ method due to Gopinathan, Whitehead, and Bogdanovic are shown to give wave functions of Hartree-Fock accuracy. The orbitals obtained with the modified $\alpha$ values reported by Gazquez and Keller give slightly higher energies.

The critical binding properties of a nostationary finite dipole rotor, explored earlier, are shown in the case of the nonphysical but mathematically interesting point-dipole rotor, to collapse back to the familiar properties of the stationary point dipole.

The broadening and shift of several Rb $3S-\mathrm{nS}$ and $3S-\mathrm{nD}$ transitions perturbed by inert gases have been measured by Doppler-free two-photon absorption and fluorescence detection. The measured shifts are in reasonable agreement with the theoretical predictions, whereas the measured broadening rates are found to be much larger.

Intensity fluctuations of the amplified-spontaneous-emission (ASE) output of a saturated 3.51-μm xenon-helium cw gas-laser amplifier have been characterized by measurements of the first seven normalized cumulants of the intensity probability distribution function (IPDF) for a single linear polarization. ASE output at all amplifier lengths measured (60 to 200 cm) displays some degree of gain-saturation distortion of the negative exponential IPDF expected for linearly amplified spontaneous emission. At long lengths (heavy saturation) the higher cumulants [initially $\mathrm{}(n-1\mathrm{})!$ for the $n$th normalized cumulant] are substantially reduced to order unity. However, the normalized variance (second cumulant) is only slightly reduced and appears to be approaching a long-length limiting value of approximately 0.45. The output shows a high degree of spatial coherence at both long and short lengths studied.