Many precipitation patterns are associated with the formation of a sparingly soluble product at a moving reaction front. This paper describes a model which describes the transport, reaction, nucleation, and droplet-growth kinetics of the processes involved. It is established that the rapid change in the nucleation rate as a function of the supersaturation is essential for pattern formation. The model allows us to correlate details of the patterns with the various kinetic processes.

We present theoretical arguments (using mean fields and strong-coupling graphs) for a line of first-order phase transitions in the three-dimensional $\mathrm{XY}$ model with the mixed action $\beta cos\left({\nabla }_i\theta \right)+\gamma cos\left(2\mathrm{}{\nabla }_i\theta \right)$, where $\gamma \in \mathrm{}(0.35,0.40)\mathrm{}$, and verify its existence by a Monte Carlo simulation.

The characterization problem of the inverse data $T$ associated with the inverse scattering for $N$ hyperbolic equations in $n+1\mathrm{}$ dimensions, $n>\mathrm{}1\mathrm{}$, is explicitly solved. A simple relationship is found between $T$ and the scattering amplitude $S$; if $N=3\mathrm{}$, $T=S$. The potential can be reconstructed by just the solving of two hyperbolic equations in two dimensions. The $N$ wave interaction equations are reduced from $n+1\mathrm{}$ to two spatial dimensions.

We investigate the kinetics of a coagulation process involving two distinct bifunctional monomeric species $A$ and $B$ (which can be ascribed a positive and negative "charge," respectively) with bonding allowed only between $A$ and $B$. When the rates for charged-charged, neutral-neutral, and neutral-charged reactions are all distinct, we find, from the solution to the mean-field rate equations, that (i) the kinetic exponents are nonuniversal and (ii) a scaling description of the clustersize distribution fails. Similarly intriguing results are also found for the kinetic behavior below the upper critical dimension.

Numerical calculations for a model anharmonic system interacting with a laser are used to analyze the quantum mechanical implications of classical structure in stochastic regions due to cantori (associated with the breakup of invariant Kolmogorov-Arnol’d-Moser surfaces). The numerical results show that a quantum wave packet may remain localized, even though classical orbits are strongly chaotic. Consequently, the quantum dynamics continues to exhibit ‘‘tunnelinglike’’ behavior even when diffusion is not classically forbidden.

It is pointed out here that a coherent state propagating through an amplitude dispersive medium will, under suitable conditions, evolve into a quantum superposition of two coherent states 180° out of phase with each other. The response of a homodyne detector to this superposition of macroscopically distinguishable states is calculated. Signatures which an experimentalist might look for in the homodyne detector’s output in order to verify the generation of such states are described.

Dynamic behavior of Brownian particles close to a wall is studied by photon correlation from an evanescent wave with variable penetration depth. Surface correlation spectra strongly differ from the bulk measurements and are completely interpreted in terms of the combined wall’s mirror effect and evanescent-wave geometry. Relevance of these new effects to the light-scattering study of surface dynamics is discussed.

A limit is established for the violation of the equality of passive and active gravitational mass. Our test is based on an asymmetry in the composition of the moon. We hypothesize that the 2-km offset between the moon’s center of figure and center of mass indicates an asymmetry in the distribution of Fe and Al. Unless the Fe on one side and the Al on the other attract each other with the same force, the moon will not be in the orbit predicted by classical mechanics. Using the results from laser ranging and a model for the moon’s interior we find that the ratios of active to passive mass for Fe and Al are the same to a precision of 4×${10}^{\mathrm{-}12}$.

Quantum analogs of Kolmogorov-Arnol’d-Moser tori and chaos in a periodically pulsed single-spin system are studied in the semiclassical regime. Wave functions (quasienergy states) are described in a spin-coherent state representation. Their projected binary-phase patterns are characterized in terms of the fractal dimensions of their perimeters.

An algebraic treatment of continuous spectra based on noncompact groups is extended to allow discussion of dissociation from bound states. Transition matrix elements between bound and continuum states can be evaluated algebraically by the construction of transition operators that transform according to the infinite-dimensional unitary representations of the noncompact dynamical group. The method is employed to calculate dissociation rates in the Morse potential, for which the relevant group is SO(2,1).

A theory for the Helmholtz free-energy functional F of inhomogeneous simple liquids is presented in which hard-sphere perturbation theory is utilized to separate F into primarily entropic and internal-energy contributions. The entropy of the hard-sphere reference system is obtained from the weighted-density approximation and the internal energy is determined from an expansion about the uniform-liquid value. The thermodynamic functions of a model Lennard-Jones solid, liquid, and vapor are then calculated and the resulting ρ-T phase diagram is found to be in good agreement with all aspects of simulation studies, including the Lindemann parameter along the freezing curve.

When diatomic nuclear motion is described in an adiabatic approximation by a guage field, the conserved angular momentum possesses a nonkinematical contribution. The present work derives this expression and, by a change of basis, gives a simple form for the addition.

An irreversible kinetic surface-reaction model, based upon the reaction of carbon monoxide and oxygen on a catalyst surface, is presented. It is found by computer simulation that the adsorbed molecules on the surface undergo both first- and second-order kinetic phase transitions. These transitions correspond to the "poisoning" phenomenon seen on catalysts. Interesting transient and periodic behavior is also seen.

A generalized resonance-tunneling equation containing a first-derivative term having the coefficient $\alpha >~0$ is found to exhibit stimulated emission of waves by the resonance. The expected Budden absorption occurs for $\alpha =2N$, $N=0,1,2,\cdots ·$. However, in bands centered around $\alpha =2N+1\mathrm{}$, the modulus of the reflection coefficient can be larger than unity.

A simple numerical reversibility test which proves useful in exposing the chaotic nature of classical dynamical systems is applied to the quantum model of a hydrogen atom in a microwave field. The remarkable result is that, in spite of some apparent chaotic features, the quantum motion proves to be perfectly stable in contrast to the high instability of the classical chaotic motion.

For thermal neutrons we have measured the Fizeau effect to 1.5% accuracy. The quoted accuracy was achieved by use of a newly designed neutron interferometer. Four fast-moving samples, all parts of a single, four-winged, aluminum, rotating propeller, could be made to engage simultaneously in the interfering beams. Our experiment complements and exceeds two recent Fizeau experiments, one of which was performed with cold neutrons and much lower accuracy and the other with a moving medium inside stationary boundaries resulting in a null Fizeau effect.

The method of finite elements converts the operator Heisenberg equations that arise from a Hamiltonian of the form $H=\frac{p^2}{2}+V\left(q\right)\mathrm{}$ into a set of operator difference equations on a lattice. The equal-time commutation relations are exactly preserved and thus are consistent with the requirements of unitarity. We consider general Hamiltonians of the form $H(p,q)\mathrm{}$ and show that the requirement of unitarity uniquely determines the operator ordering in such Hamiltonians. (The ordering procedure involves a set of orthogonal polynomials which are not widely known.) Our result shows that it is possible to treat quantum spin systems by the method of finite elements.

We show that the Fourier transform of very complex spectra gives a sound measurement of long-range statistical properties of levels even in cases of badly resolved, poorly correlated spectra. Examples of nuclear energy levels, highly excited acetylene vibrational levels, and singlet-triplet anticrossing spectra in methylglyoxal are displayed.

The 1D Hubbard model is shown to be an exactly integrable system. A "covering" model of 2D statistical mechanics which I proposed recently was shown to provide a one-parameter family of transfer matrices, commuting with the Hamiltonian of the Hubbard model. I show in this work that any two transfer matrices of a family commute mutually. At the root of the commutation relation is the ubiquitous Yang-Baxter factorization condition. The form of the $R$ operator is displayed explicitly.

A recent result concerning the assignment of well-defined values to certain noncommuting observables in quantum ensembles which have been both preselected and post-selected appears to show that quantum mechanics is "contextual." Extending the argument to the case of measurements on two separated spin-½ systems suggests that quantum mechanics is nonlocal. The significance of these phenomena is evaluated, and it is shown that they have no bearing on the question of contextuality or nonlocality.