Statistical fluctuations in linear quantum-mechanical systems are shown to result from a projection of the total quantum system onto a restricted subspace. The resulting equations of motion are of the generalized Langevin form, with fluctuating and dissipative terms. These terms are related by a quantum-mechanical fluctuation-dissipation relation that ensures thermal equilibration. We analyze the dynamical behavior of the subsystem and elucidate the meaning and interrelation of several ubiquitous concepts in the following context: weak-coupling limit, Markovian limit, rotating-wave approximation (RWA), and low-temperature behavior. The three most salient consequences of our analysis are as follows: (1) The time scale for the correlation of fluctuations and the dissipation can be quite distinct, (2) the traditional implementation of the RWA only gives valid results in the strict weak-coupling limit, and (3) a reformulation of the RWA valid at arbitrary coupling strengths, and hence at arbitrarily low temperatures, is possible.

A density-functional description of liquid crystals is developed. Formally exact expansions for thermodynamic functions in terms of a direct-correlation function are given. Approximations to the direct-correlation function lead to different versions of the molecular-field theories of liquid crystals. The properties of the uniform nematic phase including the isotropic-nematic phase transition at constant pressure are discussed. Expressions are given for the change in density and order parameters at the transition in terms of the direct-correlation function of the isotropic phase. Methods for calculating the direct-correlation functions of the isotropic phase are also discussed. A formal theory for the statistical mechanics of a nonuniform liquid crystal is developed and used to derive expressions for the Frank elastic constants. This approach provides a starting point for the investigation of the phase transitions in the liquid crystals and the properties of inhomogeneous systems. A microscopic description of the Landau—de Gennes theory is also given.

The rotating harmonic oscillator in three dimensions (owing its relevance to the diatomic molecule) has been reinvestigated by Nieto and Gutschick. They have demonstrated that the ground-state energy, which is expected (on the basis of naive arguments involving the uncertainty principle) to acquire a contribution $\frac{1}{2}\hslash \omega$ from each degree of freedom, and hence should have a value $\frac{3}{2}\hslash \omega$, does, on the contrary, in the limit of large equilibrium separation (between the atoms), go to the asymptotic value of only $\frac{1}{2}\hslash \omega$, thereby violating what these authors called a "quantum folk theorem." The present Brief Report consists of showing that these conclusions can be elucidated analytically and further extended through the $\frac{1}{N}$ expansion ($N$ being the dimensionality of the space), leading, in particular, to the result that for the case $N=2\mathrm{}$ the approach to the asymptotic limit $\left(\frac{1}{2}\hslash \omega \right)$ is, surprisingly, from below, thereby providing an even stronger violation of this type of "equipartition theorem."

A molecular two-state model, including translation factors, is used within the "quasidiatomic" approximation to calculate the differential charge-transfer probabilities in ${\mathrm{H}}^{+}$ -${\mathrm{H}}_2$ collisions at 3° laboratory scattering angle. The essential features of experiment are reproduced.

Effects on the collision dynamics due to the inclusion of the Coriolis term in the time-dependent Hartree-Fock Hamiltonian are investigated for the ${\mathrm{He}}^{2+}$ + He colliding system both at low and high incident energies. Whereas at low energies these effects are perturbative, Coriolis terms produce drastic reductions in charge-exchange cross sections at high energies.

The continuum intermediate-states approximation has been used in the evaluation of cross sections for electron capture by ${\mathrm{Li}}^{+1\mathrm{}}$ ($1s^2$), ${\mathrm{Li}}^{+2\mathrm{}}$ ($1s$), and ${\mathrm{Li}}^{+3\mathrm{}}$ ions from hydrogen atoms within an ionic energy range of $200\mathrm{keV}<~E<~10000\mathrm{keV}$. For each projectile system, the total capture cross sections were compared with the results of Shah, Goffe, and Gilbody [J. Phys. B 11, L233 (1978)] over a quoted experimental range $65\mathrm{keV}<~E<~1500\mathrm{keV}$.

In an electron-photon coincidence experiment the angular dependence of the photon linear polarization in the elementary process of atomic-field bremsstrahlung was measured for fixed direction and energy of the outgoing electron and for coplanar geometry. An electron beam of 300 keV was used, incident on copper and gold targets. It was found that for photon-emission angles with large cross section the radiation is almost completely polarized with the electric vector in the reaction plane. A decrease of the polarization caused by electron spin-flip radiation was observed for a photon-emission angle near the minimum of the cross section. The measurements are compared with theoretical calculations.

The form factor is a key parameter to be evaluated in most theoretical approaches currently available for the calculation of inelastic collisional cross sections involving Rydberg atoms. The binary-encounter method is shown to offer a very powerful means for the rapid evaluation of this parameter. Analytical expressions of the form factor are derived from hydrogenic wave functions. Many comparisons between binary-encounter and quantal calculations establish the range of validity of the former method. It is shown that, in most situations of practical interest, this approach provides an easy and efficient way to compute the cross sections corresponding to inelastic collisions between Rydberg atoms and atomic or molecular targets.

We formulate the quantum theory of stimulated Raman scattering in three dimensions. The spatial coherence function of the Stokes pulse is found as a function of the Fresnel number. The pulse-energy distribution function is calculated and compared with recent measurements.

Various characteristics of dynamical electric fields in strongly coupled equilibrium one-component plasmas are inferred from the dynamical structure factor $S(\overrightarrow{\mathrm{k}},\omega )$ obtained in molecular dynamics experiments. The energy density due to all the fluctuations generated by $S(\overrightarrow{\mathrm{k}},\omega )$, narrowly peaked near the plasma frequency, is estimated, and found to be a significant fraction of $\mathrm{nT}$, ($n$=density, $T$=temperature in energy units). The resulting macroscopic field seen by the radiating atom is argued to be an oscillation at the plasma frequency with a slowly varying amplitude when the dispersion $(\omega \mathrm{vs} \overrightarrow{\mathrm{k}}$ is negligible, and a sum of fields with slowly varying amplitudes and a spread in frequencies when the dispersion is significant.

For a metallic system of ions with interaction potentials of the general form given by pseudopotential theory, and with the motion of the ions treated by classical statistics, strain derivatives of the canonical partition function are constructed. Expressions are obtained for the stresses and isothermal elastic constants, for any crystal in which there are no sublattice displacements accompanying a homogeneous deformation. These expressions are in the form of canonical-ensemble averages, and can be evaluated by standard computer simulation techniques. The nature and magnitude of quantum corrections are discussed.

Informational entropies $S_{\rho }=-\int \rho \ln \rho d\overrightarrow{r}$ and $S_{\gamma }=-\int \gamma \ln \gamma d\overrightarrow{\mathrm{p}}$ have been computed from neutralatom Thomas-Fermi coordinate-space density $\rho$ and momentum density $\gamma$. These entropies turn out to be $S_{\rho }\simeq N(5.59-2\mathrm{}\ln N)$ and $S_{\gamma }\simeq N(1.06+\ln N)$ leading to $S_{\rho }+S_{\gamma }\simeq N(6.65-\ln N)$, strikingly similar in form to the rigorous bound $S_{\rho }+S_{\gamma }>~3N(1+\ln \pi )-2N\ln N$ due to Bialynicki-Birula and Mycielski. It is conjectured that the informational entropies for atoms may be well represented by $S\simeq N(\alpha +\beta \ln N)$, $\alpha$ and $\beta$, being universal constants.

The time-correlation functions characterizing linear viscoelasticity and nonlinear transport in shear flow are compared for a low-density gas of Maxwell molecules. It is shown that the relationship between viscoelasticity and nonlinear transport given by the Goddard-Miller rheological equation of state does not apply, and the principle of objectivity on which this equation is based is not valid.

From the heat-capacity studies of several different liquid-crystal compounds, each with an isotropic ($I$)-smectic-$A$ ($\mathrm{Sm}A$)-smectic-$C$ ($\mathrm{Sm}C$) [or chiral-smectic-$C$ (${\mathrm{Sm}C}^{*}$)] transition sequence, one possible general behavior is found between $t_0$ and $\frac{T_{\mathrm{AC}}}{T_{\mathrm{IA}}}$. Here $T_{\mathrm{AC}}$ and $T_{\mathrm{IA}}$ denote the $\mathrm{Sm}A-\mathrm{Sm}C(-{\mathrm{Sm}C}^{*}$) and $I-\mathrm{S}\mathrm{m}A$ transition temperatures. The important parameter $t_0$ characterizes the full width at the half-height of the mean-field heat-capacity anomaly associated with the $\mathrm{Sm}A-\mathrm{S}\mathrm{m}C$ or $\mathrm{Sm}A-{\mathrm{Sm}C}^{*}$ transition and features the crossover from an ordinary mean-field-like behavior to a mean-field-tricritical-like behavior as the temperature of the system moves away from the transition temperature.

The pair-correlation function for a binary ion mixture is derived to second order in the plasma parameter by using a recently proposed method, based on the quadratic fluctuation-dissipation theorem. A substantial difference between the pole structures in the complex $k$ plane of this correlation function and that of the one-component plasma is conjectured.

We find a general expression for the effective charge $Z_{\mathrm{eff}}$ of slow ions in dilute plasmas at temperature $T$, which applies for atomic numbers $5<~Z_1<~92$. The ratio $\frac{Z_{\mathrm{eff}}}{Z_1}$ becomes a function of $\frac{T}{Z_1^2}$. The effective-charge dependence of the collision logarithm for slow ions in the plasma is analyzed. A transition from classical to quantum regimes occurs with increasing $T$, for $\frac{T}{Z_1^2}\approx {10}^6$ K. The effective ion charge is relevant in the classical domain. For temperatures across and over the transition the ions are fully stripped of electrons.

The effects of position-dependent dipole-dipole frequency shifts are included in a semiclassical description of resonance fluorescence from many two-level atoms in a volume small compared with a resonant wavelength. In general, these effects are drastic: They lead to loss of coherence long before cooperative effects become important. In samples for which the field of a uniform polarization is itself uniform we obtain criteria for the stability of the Bloch vector against dipolar-induced dephasing.

Anharmonic effects on the critical dynamics of two-dimensional anisotropic melting arising from the existence of a large regime of smecticlike behavior right above the melting temperature are studied and shown to be irrelevant, despite the strong relevance of such effects for three-dimensional smectics. This irrelevance is due to the finite persistence length of smectic fluctuations in two dimensions.

A general upper bound is obtained for the nonexponential contribution to the time-dependent occupation amplitude $G\left(t\right)\mathrm{}$ for an autoionizing state just above the continuum threshold in the limit of narrow widths. This upper bound is shown to be inconsistent with some recently published results predicting new observable nonexponential effects in ${\mathrm{}\left|G\right(t\left)\right|}^2$, but is consistent with earlier long-accepted theory. It is also shown how some nonexponential contibutions to the decay might, in principle, still occur as a consequence of close proximity between the autoionizing state and the ionic threshold, although these contributions now have a different form than those recently proposed.

The apparent enhancement in the extent of the reaction ${\mathrm{N}}_2$${\mathrm{O}}_4$ → ${2\mathrm{N}\mathrm{O}}_2$, dissolved in near-critical ${\mathrm{CO}}_2$, an effect measured by Krichevskii, is reconsidered. The data are shown not to be consistent with the enhancement predicted by Procaccia and Gitterman. It is further shown that the entire effect can be quantitatively accounted for as a consequence of critical turbidity. It is concluded that Krichevskii's data cannot be used as an example of the proposed effect of critical points on the extent of a reaction and that great care should be taken when interpreting any data where the effect seems to appear.