Given that two initially independent systems A and à are in a pure state, we study the type of interaction between them that will lead an observer, limited to measuring system A only, to conclude that it is in a thermal bath. We show (under rather mild conditions) that there is always an interaction that does it, and study it for two particularly simple systems.

A recent model for positional ordering in systems of monodisperse parallel hard spherocylinders is used to calculate the pressure over the entire range of densities and cylinder axial ratios. Reasonable quantitative agreement with Monte Carlo data is obtained for the full spectrum of nematic, smectic, columnar, and crystalline order. Analytical expressions are also given for the characteristic lengths of the ordering in these phases.

A three-dimensional anisotropic Ising spin model with nearest-neighbor interactions in all spatial directions supplemented by a four-spin interaction along one axis only is treated within a generalized mean-field approximation including short-range correlations. In obtaining the phase diagram various ordered structures are discussed. The results suggest that, besides the ferro- or antiferromagnetic and the so-called 〈3,1〉 phase, no additional modulated phases appear. The order-disorder transition temperature is finite everywhere, with both first- and second-order transitions present.

By using the technique of optical second-harmonic generation, we have succeeded in obtaining the orientation, spectrum, and the change in dipole moment upon optical excitation for monolayers of retinal chromophores, which are of relevance for visual excitation. The change in dipole moment of the chromophore embedded in the purple membrane of Halobacterium halobium is found to be identical to that of the free chromophore. The spectrum of all-trans retinal monolayers exhibits a subsidiary one-photon forbidden peak in addition to the main absorption peak.

Expressions for differential and total cross sections for atom-diatom scattering are derived using the impulse formalism without any approximations. Results for the rotational-vibrational scattering are obtained without using the peaking approximation (PA). For the specific case of a hard-core potential, it is shown that, except for elastic scattering, PA results are substantially different from the true impulse results.

We have studied the autoionization decays of the nd ${}_{}{}^1{}_{}{}^{}\mathrm{\Lambda }_{\mathrm{g}}^{}{}_{}{}^{}$ Rydberg states of ${\mathrm{Na}}_2$ in the presence of a low electric field. Under certain conditions, we observe signals having a humped shape departing largely from the usual exponential behavior. These decays are described by a simple model which accounts for the interactions with both discrete and continua levels. It is shown that these decays are the time signature of the optical excitation of complex resonances.

We investigate the effects of electronic autoionization on the vibrational branching ratios in resonant multiphoton ionization of ${\mathrm{H}}_2$. Ab initio calculations are performed to obtain the vibrational branching ratios for (3+1) resonant-enhanced multiphoton ionization (REMPI) of ${\mathrm{H}}_2$ via the C ${}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ state. Our calculations include the effects of the dissociative ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }_{\mathrm{g}}^{}{}_{}{}^{}$(1${\mathrm{\sigma }}_{\mathrm{u}}$1${\mathrm{\pi }}_{\mathrm{u}}$) autoionizing state and properly account for the interference between the direct and the indirect (autoionization) channels. We find that the direct and indirect amplitudes are comparable for excitation via the higher ($v_i$≥2) vibrational levels of the C state. Autoionization greatly enhances the branching ratios for Δv≠0 transitions. These calculations underscore the necessity for a proper treatment of both the direct and indirect contributions in understanding the REMPI of molecules via autoionizing states.

An experimental technique which permits the study of single three-level atoms prior to quantum jumps to a shelving state has been used to study the second-order photon statistics of laser-excited barium atoms. Measured values of Mandel’s Q parameter agree with the theory derived for two-level atoms. This result illustrates the extent to which the presence of additional levels can be ignored in certain systems: Although the third level in this system is responsible for the quantum jumps, prior to each jump the system’s behavior is within experimental errors, exactly like that of a two-level atom. The negative values of Q obtained for a range of laser intensities demonstrate the sub-Poisson character of the emission.

The time evolution of photon statistics is solved for a mode of damped electromagnetic field in an arbitrary state. It is shown that the cavity dissipation changes the photon number variance but does not affect the normalized second-order correlation function. The lifetime of a pure number (Fock) state ‖m〉 is found to be only one mth of the photon lifetime.

We have carried out Brownian dynamics simulations to measure the self-diffusion of charged colloids in the presence of an oscillating shear flow. We observe that in the two directions perpendicular to the shear velocity direction, the diffusion constant increases monotonically with the shear rate γ. We also find a slight layering along the shear direction. Our results are compared to the forced Rayleigh scattering experiments of Qiu et al. [Phys. Rev. Lett. 61, 2554 (1988)].

We directly measure the fractal dimension $D_A$ of the accessible perimeter for diffusion limited aggregation. We find $D_A$=D, where D is fractal dimension. Moreover, the number of inaccessible sites also scales as the mass of the entire aggregate, stabilizing at (36–37) % of the total perimeter after a short transient. Hence, the well-known anomalies in the multifractal analysis of the growth probability distribution are not a result of the possibility $D_A$

We study the moments of displacement of a diffusing particle in one dimension in the presence of correlated random fields. We find that even for short-range algebraic correlations there exists a critical moment $q_c$ such that for q<$q_c$ the moments of displacement depend logarithmically on time, whereas for q>$q_c$ the moments of displacement are a power law of time. This result is surprising since usually short-range correlations do not change the scaling properties.

The properties of polymers in a disordered environment are studied with emphasis on the effect of trapping due to fluctuations in the porosity of the environment. Results are obtained for $Z_N$, the number of self-avoiding walks of length N starting at the origin, and D, the diffusion coefficient for the center of mass of the polymer. The two most important new results are that 〈ln$Z_N$〉≊N-$a_1$$N^{\alpha }$, with α=2-dν and ν the Flory exponent, and that the leading behavior of the diffusion coefficient is D≊exp(-$a_2$$N^{\alpha }$).

We have measured the fractal dimension of radial fingering patterns in a smooth Hele-Shaw cell over a range of almost 2 orders of magnitude in the dimensionless driving force. After taking on the diffusion-limited-aggregation dimension 1.71 through much of the lower half of the observed range, the dimension reaches an apparent asymptotic value of 1.79±0.04 through the upper half. No evidence of progress toward a dense-branching morphology is observed in the range of this experiment.

The variation with deposition voltage of the electrical resistance of copper electrodeposits in a paper support has been examined by direct ac measurement. Intensive contributions to the resistance of the deposits, such as the cross-section area of the branches and microcrystalline habit, increase from the low (0.6 V versus a copper reference electrode) to mid- (2.0 V) range of the voltages studied. Examination by scanning electron microscopy reveals distinct differences at the micron scale between the deposits. These differences appear to explain the changes in the intensive resistance contributions.

Extensive variational calculations using Hylleraas-type functions are carried out on the ${}_{}{}^2{}_{}{}^{}\mathrm{S}$ ground states for the following members of the Li i isoelectronic series: Li i, B iii, C iv, N v, O vi, F vii, and Neviii. For each species, the nonrelativistic energy, the electronic density at the nucleus, the specific mass shift, the transition isotope shift, the Fermi contact interaction, the diamagnetic susceptibility, the nuclear magnetic shielding factor, moments of 〈$r_i^n$〉 for n=-1, 1, 2, and 3 and of 〈$r_{\mathrm{ij}}^n$〉 for n=-1, 1, and 2 are reported. The nonrelativistic energies obtained are lower than any previously published values for each member of the Lii series examined. The effect of one versus two spin eigenfunctions in the basis set is examined. The rates of convergence for both the one- and two-spin-eigenfunction basis sets are examined for each expectation value.

A procedure for the Feshbach projection is presented. Although projection operators are not explicitly used within this procedure, it is completely equivalent to an explicit use of idempotent projectors, provided that both the target-state wave functions and the trial function of the entire system are of the configuration-interaction type. The Feshbach-projection-operator method is extended to the case of triply excited resonances (i.e., to an infinite number of open channels). Projectors are given explicitly for three-electron systems and for N-electron systems with the double-ionization threshold described by the (N-2)-electron one-determinant function. For configuration-interaction wave functions a procedure similar to that for doubly excited states is proposed.