The scheme of bifurcations in systems described by a certain class of delay-differential equations is investigated in detail. It is shown that higher-harmonic oscillating states appear successively in the course of transition to developed chaos. First-order transitions between these states account for the frequency-locked anomaly recently observed by Hopf et al. in a hybrid optical bistable device.

Bell's theorem is formulated as a nonlocality property of quantum theory itself, with no explicit or implicit reference to determinism or hidden variables. A recent Letter on this subject is discussed.

Arguments are given against considering Bell's inequalities to be equivalent with determinism. Possible misinterpretations of the conflict between quantum mechanics and these inequalities are pointed out. With use of results obtained in previous papers on this subject, it is shown that locality rather than determinism is the issue.

A classical analysis is presented of the microwave perturbation of electrons bound to the surface of liquid helium by their image charge. Since the classical dynamics can exhibit chaotic behavior, this one-dimensional quantum system provides a novel system for the experimental investigation of quantum stochasticity. Analytic estimates for the classical thresholds and rates for stochastic excitation and ionization are determined as functions of microwave field amplitude and frequency. The frequencies and powers required to study stochasticity in the quantum regime are readily available.

A model of a simple nonlinear physical system, the driven diode resonator comprised of an oscillator, resistor, inductor, and diode in series, is shown to reduce exactly to a one-dimensional, noninvertible map. With use of a model of the diode which includes the forward bias voltage, reverse recovery time, and junction capacitance, the response of the system is calculated exactly. The solution exhibits the period-doubling route to chaos with universal scaling.

The nucleation rate in a supersaturated Glauber-kinetic lattice gas of size ${168}^3$ is measured as a function of supersaturation (magnetic field). Results at $\frac{T}{T_c}=0.59\mathrm{}$ are roughly compatible with classical nucleation theory. The droplet surface tension for the critical nuclei, determined from the observed cluster numbers, shows no sharp spinodal point and is nearly independent of the field.

The $d=2\mathrm{}$ $\mathrm{XY}$ model is generalized to include an operator that couples directly to the vortex core energy, while maintaining the full symmetry of the original model. In addition to the usual Kosterlitz-Thouless transition, the model exhibits a true first-order transition and a pseudo first-order transition. The excitations of the model include fractionally charged vortices. Implications for the $d=2\mathrm{}$ melting problem are discussed.

Subharmonic bifurcations, generalized multistability, and chaotic behavior were found experimentally in a $Q$-switched C${\mathrm{O}}_2$ laser operating at 10.6 μm. Jumps between two strange attractors lead to a low-frequency ($\frac{1}{f}$ type) divergence in the power spectrum. This is the first experimental evidence of these phenomena in a quantum-optical molecular system. A theoretical model is also presented whose results are in good agreement with the experimental data.

A counterexample is given to a recent suggestion that if the inequalities of Clauser and Horne hold, then there exists a hidden-variable model for a spin-½ correlation experiment of the Einstein-Podolsky-Rosen type.

The dynamics of interfaces where the normal component of an interface velocity is proportional to the curvature is studied. The dynamic structure function due to the motion of random interfaces is shown to satisfy a scaling law. The results are compared with Monte Carlo simulations of the kinetics of the order-disorder transition in a quenched system.

Transverse electromagnetic waves possessing finite energy, action, and $\int \overrightarrow{\mathrm{E}}·\overrightarrow{\mathrm{B}}{d}^{4}x$ are obtained in 3 + 1 dimensions as a solution of the source-free Maxwell's equation in vacuum.

Baxter has solved a restricted class of square lattice gas models with nearest-neighbor exclusion (thus "hard squares") and next-nearest-neighbor interactions. Arguments are presented which demonstrate that the subspace spanned by his exact solution contains the line of tricritical points and the associated surface of first-order transitions of hard squares with attractive next-nearest-neighbor interactions. The tricritical exponents so identified confirm those obtained by Nienhuis for a dilute Ising model.

An improved perfect-fluid energy-momentum tensor including spin and torsion is presented with use of a Lagrangian variational principle based upon the tetrad formalism of Halbwach and the method of constraints of Ray.

A two-dimensional $n$-component spin model with cubic or isotropic symmetry is mapped onto a solid-on-solid model. Subject to some plausible assumptions this leads to an analytic calculation of the critical point and some critical indices for $-2\mathrm{}<~n<~2$.

It is shown that the new interpretation of the scalar product in Hilbert space recently proposed by Aharanov, Albert, and Au is in fact the one underlying the stochastic phase-space formulation of nonrelativistic quantum mechanics. The extrapolation of this interpretation to the relativistic domain and its relationship to the program of geometrizing quantum theory and quantizing space-time are discussed.

A new symmetry-adapted perturbation theory is suggested with the following improved properties: The primitive function is localized, and for Coulomb potentials has only a single cusp; the modified equation has no spurious bound states. A systematic tight-binding perturbation expansion involving only two-center integrals is derived.

An orthogonalization process is proposed, applicable to spaces which are realizations of abstract Hilbert space. It is simpler than the Gram-Schmidt process. A recurrence relation which orthogonalizes a physical space is proposed and it is shown that the generalized Langevin equation is contained therein. This process serves as a basis for understanding the nature of the dynamic many-body formalism.

Composites formed from charged particles and vortices in (2+1)-dimensional models, or flux tubes in three-dimensional models, can have any (fractional) angular momentum. The statistics of these objects, like their spin, interpolates continuously between the usual boson and fermion cases. How this works for two-particle quantum mechanics is discussed here.

The directed-site animal problem on the square and triangular lattices is shown to be equivalent to Baxter's hard-square lattice-gas model with anisotropic next-nearest-neighbor interactions at a disorder point. The exact solution of the latter is used to determine the animal numbers as functions of their size in the two cases. Expressions in closed form are proposed for the number of animals on an infinite strip in terms of width and animal size, and for the average transverse extent of animals of a given size.

Some new, powerful, and very simple Bell inequalities are derived. They establish that for two spin-$s$ particles in the singlet state, the quantum-theoretic Einstein-Podolsky-Rosen correlations for spin measurements along all pairs of directions from a set of $N$ axes are incompatible with local realism for any set of distinct coplanar axes when $N=3\mathrm{}$, and for any set of distinct axes whatever when $N=4\mathrm{}$, with the possible exception of sets restricted by one of the constraints $\hat{a}\pm \hat{b}\pm \hat{c}\pm \hat{d}=0\mathrm{}$. These results hold for any value of the spin.