Fluctuation formulas which are characteristic of the classical isoenthalphic-isobaric ensemble are derived in a direct and fundamental way. The technique used is adapted from a new method introduced by Pearson, Halicioglu, and Tiller [Phys. Rev. A 32, 3030 (1985)] in their treatment of the microcanonical ensemble. The application of this new method to other adiabatic ensembles is also discussed.

It is shown that a smooth stationary distribution can be derived for ‘‘coarse-grained’’ repellers by compensating the local escape. This provides a convenient framework to investigate statistical properties of long chaotic transients. Furthermore, our procedure yields a powerful tool for calculating fractal dimensions.

In this comment we study the problem of the stimulated recombination in an open system from a stochastic point of view. We set up the bivariate master equation for the number of photons and ions inside the system. Then we perform a systematic expansion, with the system volume as an expansion parameter, and we obtain the fluctuations of the number of photons and ions around its macroscopic values in the linear noise approximation; the stationary solution is also investigated.

We discuss why the five chiral terms in the elastic energy for a biaxial nematic liquid crystal proposed recently cannot occur simultaneously due to topological constraints. We argue, however, that twist about only one axis is possible. We also show that our expression for the elastic free energy of a biaxial nematic liquid crystal reduces easily to that of a uniaxial nematic liquid crystal.

The irrelevance of topological constraints for the construction of the distortion free-energy density of biaxial nematic liquid crystals is discussed.

Recent magnetic birefringence experiments have measured the temperature difference $T_0$-$T^{\mathrm{*}}$=ΔT as a function of concentration (amphiphile volume fraction φ) for the micellar system cesium perfluoro-octanoate–water. Here $T_0$ is the isotropic-nematic transition temperature and $T^{\mathrm{*}}$ is the ‘‘Landau’’ temperature at which the birefringence (and light scattering intensity, etc.) would diverge if the first-order phase transformation did not intervene. By treating explicitly the competing roles of attractive and repulsive forces, we account for ΔT being much smaller than that in thermotropic liquids and for its strong increase with φ.

μ-α sticking probabilities have been calculated for the S state and the P state, using a high-precision three-body variational wave function. The 0.90% S-state sticking probability agrees with previous works using other methods. It is necessary to calculate two sets of sticking probabilities and fusion rates for the J=1, ν=0 state, from which an effective sticking probability of 0.31% is calculated. As in all previous calculations, the traditional sudden approximation is used whenever possible. In addition, it is necessary to average the sticking probability over a small region of nuclear influence instead of evaluating it at the point of nuclear coalescence.

Coupling effects among the channels for collisional excitation of 2$s^2$2$p^4$, 2s2$p^5$, and 2$p^6$ configurations of oxygenlike krypton have been investigated by comparing six-, five-, four-, three-, and two-state close-coupling (CC) cross sections for the electron collision energy range 26.2 Ry≤E≤500 Ry. We discovered the surprising result that the calculated three-state CC (3CC) cross sections for the transition from the ground state to the 2$p^6$ ${\mathrm{}}^1$$S^e$ and the two-state CC cross section to the other excited states are reduced [considerably (45%) for the former] when the 2s2$p^5$ ${\mathrm{}}^3$$P^o$ channel is added to the 5CC approximation. In addition, the 3CC cross section σ(2$p^4$ ${\mathrm{}}^3$$P^e$–2$p^6$ ${\mathrm{}}^1$$S^e$)is diminished by a factor of 100 at 26.2 Ry by the addition of the 2s2$p^5$ ${\mathrm{}}^3$$P^o$ state. Approximations which omit the 2s2$p^5$ ${\mathrm{}}^3$$P^o$ state overestimate the cross sections.

Resonant transfer and excitation (RTE) involving simultaneous electron capture and projectile K-shell excitation has been measured for calcium ions in charge states ranging from neonlike to hydrogenlike incident on molecular hydrogen over an energy range 100–370 MeV. The results establish a projectile charge-state dependence for RTE and provide a detailed test of theoretical calculations. The effect of the target-electron momentum distribution on the RTE process is demonstrated by comparing with previous results for calcium ions incident on helium.

Quantum-mechanical interference is found in the two-photon excitation of an atomic ${}_{}{}^1{}_{}{}^{}\mathrm{S}$ through the nonresonant sequence ${}_{}{}^1{}_{}{}^{}\mathrm{}_{}^1{}_{}{}^{}$P←${\mathrm{}}^1$S, since the magnetic sublevels of the intermediate ${}_{}{}^1{}_{}{}^{}\mathrm{P}$ state provide multiple pathways for absorption. Depending on the relative polarization of the two incident light beams, the interference can be either constructive or destructive. When the electric vectors of the light beams are linearly polarized and orthogonal, the interference is purely destructive and two-photon transitions are forbidden. Application of an external magnetic field, however, lifts the degeneracy of the intermediate state giving a two-photon absorption rate proportional to the square of the magnetic field strength. These effects are reported for the (7s${)}^1$S←(5${\mathrm{s}}^2$${)\mathrm{}}^1$S transition of atomic Sr excited by two dye lasers operating at different wavelengths.

We describe the design and operation of a cryogenic hydrogen maser for use at temperatures below 1 K. The maser incorporates a cooled atomic hydrogen beam and cylindrical dielectrically loaded resonant cavity with liquid-He-covered walls to prevent hydrogen recombination and dephasing of the atoms’ oscillating dipole moment upon wall collisions. We have observed maser oscillation from approximately 350 to 575 mK at power levels up to 5×${10}^{\mathrm{-}13}$ W, and have measured the maser’s line Q and frequency as a function of temperature and helium-film thickness.

It is shown that originally linearly polarized light can become spontaneously circularly polarized as it propagates through a semiconductor with a pronounced two-photon–biexciton resonance. The intensity difference Δ between left- and right-hand circularly polarized light undergoes a second-order phase transition at a critical total intensity. The instability is due to the process of induced absorption from the exciton to the biexciton. It should be observable in transmission experiments through CuCl platelets or films.

Applying finite-size scaling analysis to diffusion-limited aggregation (DLA) clusters grown in finite width strips on a square lattice we find that $l_{?}$ and $l_{\perp }$, the cluster lengths along and perpendicular, respectively, to the direction of growth, diverge as &, respectively, where N is the number of particles in the cluster. We find numerically that ${\nu }_{?}$∼(2/3) and ${\nu }_{\perp }$∼(1/2). From the finite-size scaling analysis we derive the expression D=1+(1-${\nu }_{?}$)/${\nu }_{\perp }$ for the fractal dimension D of DLA clusters on a square lattice. The value D∼(5/3) predicted from this relation agrees with the expected result.

It is shown that by tuning the experimentally observable critical region, singularities of the phase boundaries can be observed in the immediate vicinity of the reentrant-nematic–smectic-C–smectic-A multicritical point. The exponents evaluated from these singularities are found to be identical to the universal exponents associated with the nematic–smectic-A–smectic-C multicritical point.

The dynamics of several model systems which display a noise-induced transition to bistability are studied in detail, focusing in particular on the question of the stability of the noise-induced stationary states. The examples exhibit a variety of phenomena in the high-noise limit deep in the bistable regime. The noise-induced states can have an infinite lifetime, a finite lifetime, or a vanishingly small lifetime. Some general results concerning the high-noise limit are reported, most notably the destabilizing effect of small correlations in the noise.

The inverse bifurcation sequence in one-dimensional maps is modified in two-dimensional ones in a universal way. Two-piece, four-piece, etc., strange attractors are eliminated one by one as the Jacobian approaches one. Renormalization theory around the Hamiltonian $T^{\mathrm{*}}$ leads to universal behavior including universal strange attractors.

The theory of neural networks is extended to include a static noise as well as nonlinear updating of synapses by learning. The noise appears either in the form of spin-glass interactions, which are independent of the learning process, or as a random decaying of synapses. In an unsaturated network, the nonlinear learning algorithms may modify the energy surface and lead to interesting new computational capabilities. Close to saturation, they act as an additional source of a static noise. The effect of the noise on memory storage is calculated.