I present and test three simple thermodynamic fluctuation rules which may in some cases hold for subsystems of infinite systems with volumes less than the correlation volume. Tests at volumes near the correlation volume are made in the two-dimensional square ferromagnetic Ising model by Monte Carlo simulation. Fluctuations into the metastable and spinodal regions are discussed. Aside from difficulties apparently resulting from the small volumes used in the simulations, the rules are found to work well.

The following cross sections for $6{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\leftrightarrow 6{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$ fine-structure mixing in Rb, induced in collisions with ground-state Rb and noble-gas atoms and with ${\mathrm{N}}_2$ molecules, have been measured using previously described methods of atomic fluorescence spectroscopy: $Q(6\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\to 6{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{})=17.3, 6.6, 6.1, 5.3, 8.5, \mathrm{and} 6.4$; $Q(6\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\leftarrow 6{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{})=11.6, 4.5, 4.1, 3.6, 5.5, \mathrm{and} 4.1$, for Rb, He, Ne, Ar, Kr, and ${\mathrm{N}}_2$, respectively, in units of ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$. Upper bounds of cross sections for the effective depopulation of the $6{}_{}{}^2{}_{}{}^{}D$ states were also determined.

New radiative lifetimes of 18 Ti ii levels are reported. They are determined by selective laser excitation of a Ti-ion beam and time-resolved observation of the fluorescence. The Ti ions are produced in a low-pressure hollow-cathode discharge. Improved absolute transition probabilities are deduced.

A mixed, atomic-and-molecular-state approach to heavy-particle collision processes is applied to electron transfer in $\alpha$-H collisions. Such collisions are difficult to treat at all impact parameters using a pure molecular-state basis without translational factors or a pure atomic-state basis (with plane-wave translational factors) at low-keV energies. It is shown that the use of translational factors in the molecular-state basis may be avoided for internuclear separations $R<~R_0$ by transforming to an atomic-state basis at $R=R_0$. This "$R$-matrix" method is shown to be stable over a range of $R_0$, and a physical criterion is given for determining $R_0$.

The evolving electronic probability density in 1-8-keV $\alpha$-H collisions has been calculated and graphed. This density is the modulus squared of the time-dependent electronic wave function in the previous coupled-molecular-state calculations of Winter, Hatton, and Lane without and with plane-wave translational factors. New, larger-basis results are also presented. The mechanism for electron transfer and the extent of sensitivity to the choice and size of the molecular basis are clearly seen in these graphs of the electron cloud.

The interference between scattered and unscattered elastic waves in beam-beam scattering is investigated in the small-angle limit. It is shown that the scattered intensity averaged over the scattering volume leads to a diminution of the forward scattering proportional to the total scattering cross section or imaginary part of the elastic scattered amplitude with angular dependence determined by the shape of the projectile and target-beam-intensity distributions. This effect cannot explain earlier observations of forward scattering enhancement observed by Geiger and Morón-León [Phys. Rev. Lett. 42, 1336 (1979)].

Angular distributions of two $K$-shell resonances in $e$-${\mathrm{N}}_2$ elastic scattering in the angular range $50°<~\theta <~150°$ have been measured in a crossed-beam apparatus. The dominant partial wave has $l=3\mathrm{}$ character, in conformity with recent theoretical predictions and photoionization measurements.

An optical-optical double resonance technique has been used on beryllium ions stored in a Penning trap to measure the magnetic dipole hyperfine interaction constant $A_{\frac{1}{2}}$ of the $2p{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ level in ${}_{}{}^9{}_{}{}^{}\mathrm{Be}_{}^{+}{}_{}{}^{}$. The measured value of $A_{\frac{1}{2}}=-118.6\mathrm{}\left(3.6\right)\mathrm{}$ MHz is in good agreement with theoretical calculations. The $2p{}_{}{}^2{}_{}{}^{}P$ fine-structure splitting and the $2s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\to 2p{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2},\frac{1}{2}}^{}{}_{}{}^{}$ optical transition frequencies have also been measured.

The widths of the $L\eta \left(L_2{M}_1\right)$ and $Ll\left(L_3{M}_1\right)$ lines of tungsten have been measured with a high-resolution 90-cm-radius bent-crystal Cauchois spectrograph. The measured values have been compared with those of earlier workers. The difference $\Gamma \left(L_2\right)-\Gamma \left(L_3\right)$ between the widths of the $L_2$ and $L_3$ levels of tungsten, as obtained from the present measurements, is in good agreement with that deduced from widths of the $L{\beta }_1\left(L_2{M}_4\right)$ and $L{\alpha }_2\left(L_3{M}_4\right)$ lines measured by us earlier. The relativistic estimates of Chen and co-workers for $\Gamma \left(L_3\right)$, $\Gamma \left(M_4\right)$, and $\Gamma \left(M_5\right)$ are found to be consistent with our linewidth measurements. However, $\Gamma \left(L_2\right)$ seems to have been underestimated by these authors, thus indicating a need for a fresh look at the relativistic estimate of the nonradiative component of $\Gamma \left(L_2\right)$ of tungsten. Our measurements further reveal that McGuire's nonrelativistic calculations have led to values of $\Gamma \left(M_1\right)$ which are too large. The situation seems to have been only partly remedied by the recent relativistic calculations of $\Gamma \left(M_1\right)$ by Chen and co-workers.

Two-photon Doppler-free spectroscopy has been used to measure Stark shifts of $n{}_{}{}^2{}_{}{}^{}S$ Rydberg states of ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$ (for $n=15\mathrm{} \mathrm{to} 80$). Scalar polarizabilities ${\alpha }_0$ were found to obey the relation ${\alpha }_0[\mathrm{in}\mathrm{MHz}/{(\mathrm{V}/\mathrm{cm})}^2]=2.202\mathrm{}\left(28\right)\mathrm{}\times {10}^{-9\mathrm{}}{n}^{*6\mathrm{}}+5.53\mathrm{}\left(13\right)\mathrm{}\times {10}^{-11\mathrm{}}{n}^{*7\mathrm{}}$, in good agreement with theoretical values. Avoided crossings were also determined, and first avoided crossings (with the $n-3\mathrm{}$ manifold of levels) fitted the relation $E(\mathrm{in}\mathrm{V}/\mathrm{cm})=4.638\mathrm{}\left(6\right)\mathrm{}\times \frac{{10}^8}{n^{*5\mathrm{}}}+1.528\mathrm{}\left(18\right)\mathrm{}\times \frac{{10}^{10}}{n^{*7\mathrm{}}}$.

We derive the most general Hamiltonian which preserves the Perelomov SU(1,1) coherent states under time evolution. It is shown that the Hamiltonian of the degenerate parametric oscillator from nonlinear optics, which does not preserve ordinary coherent states, does preserve the SU(1,1) coherent states under time evolution.

We make some pertinent comments on previous work on the adiabatic elimination in quantum optical systems.

We propose that the free energy of solids and dense liquids can be calculated by combining perturbation theory with direct evaluation of free-energy difference by Monte Carlo sampling. The method provides a novel, convenient, and direct approach to the free energy of both solids and liquids without using thermodynamic integration or upper-bound approximations. Monte Carlo perturbation results for model two-dimensional systems are shown to be in very good agreement with free energy obtained by standard techniques.

The role of spatially coherent modes in a chaotic state of the damped and driven Toda chain is investigated with the help of the scattering transform.

We propose a method of analysis of the density behavior of the experimental neutron scattering structure factor which permits us to derive directly from the experimental results an "experimental" pair potential. We apply the method to the recent results of Teitsma and Egelstaff in krypton gas and derive a pair potential which is in good agreement with the empirical potential of Barker et al. Some discrepancies in the range $4<r<\mathrm{}8\mathrm{}$ Å are noted.

A deterministic-phenomenological model for the Belousov-Zhabotinsky system is coupled with Gaussian additive noise to analyze the role of fluctuations when a dissipative structure emerges. We define a parameter $\overline{k}$ which measures the degree to which the fast-relaxing degree of freedom is "enslaved" (in Haken's terminology) to the two order parameters. We derive the center-manifold equation which gives the fast degree of freedom as a function of the slow variables. All the recurrent and locally attractive behavior of the system lies in this surface. We then derive an equation relating the relaxation time of the fast-relaxing degree of freedom, the intensity of the Gaussian noise, and the parameter $\overline{k}$. The relaxation time is taken as the reciprocal of the damping constant which depends on the bifurcation parameters of the system. The maxima in the probability density factor for the order variables coincide with the macroscopically observed states.

The role of fluctuations is studied in the locally attractive and locally invariant center manifold for a system which is a truncation of Hopf's model for hydrodynamic turbulence. The anlaysis is carried out in a regime where the system sustains a hard-mode instability and the real part of the Floquet coefficients does not change sign. The Gaussian width of the time-independent factor of the probability density is shown to measure the subordination of the fast-relaxing degree of freedom. A physically meaningful equation is derived relating the Gaussian width, the intensity of the additive noise, and the external control parameter. The characteristic curves of the reduced Fokker-Planck equation are the limit cycles derived from bifurcation theory.

Numerical simulations show the existence of an ergodicity threshold in the Fermi-Pasta-Ulam $\alpha$ model. This feature is common to a large class of nonlinear Hamiltonian systems.