It is proved that under any time-periodic Hamiltonian, a nonresonant, bounded quantum system will reassemble itself infinitely often in the course of time. To illustrate these results computer experiments are performed on both a pulsed quantum rotor and an electron in the field of periodic electromagnetic pulses.

A bifurcation diagram for a driven nonlinear semiconductor oscillator is measured directly, showing successive subharmonic bifurcations to $\frac{f}{32}$, onset of chaos, noise band merging, and extensive noise-free windows. The overall diagram closely resembles that computed for the logistic model. Measured values of universal numbers are reported, including effects of added noise.

A new interpretation of the scalar product in Hilbert space was presented recently by Aharonov, Albert, and Au. Here the essential equivalence between such a view-point and Wigner's exact reformulation of nonrelativistic quantum mechanics using distribution functions is pointed out.

Analytic studies of the Yvon-Born-Green equation have suggested that it may show no true critical region for spatial dimension $d<~4$ but that for $d>\mathrm{}4\mathrm{}$ there is a critical point of the mean-field type. Presented here are the results of numerical solution of the equation which strongly support these suggestions. Thus the Yvon-Born-Green equation exhibits the correct borderline dimensionality of four and the expected mean-field behavior for $d>~4$, but for $d<\mathrm{}4\mathrm{}$ has only a region of long, but finite, ranged correlations.

It is demonstrated that the total mass of a nontrivial isolated physical system is positive even after part of its mass has been lost because of gravitational radiation. This method is an extension of the one that the authors used in the proff of the classical positive-mass conjecture.

The positive-energy conjecture is proved at null infinity. That is, an isolated system in general relativity can never radiate away more energy than is given by its total Arnowitt-Deser-Misner energy.

It is shown that the following statements about a quantum correlation experiment are mutually equivalent. (1) There is a deterministic hidden-variables model for the experiment. (2) There is a factorizable, stochastic model. (3) There is one joint distribution for all observables of the experiment, returning the experimental probabilities. (4) There are well-defined, compatible joint distributions for all pairs and triples of commuting and noncommuting observables. (5) The Bell inequalities hold.

Newton's gravitational constant $G$ is calculated in a class of scale-invariant gauge theories with an infrared fixed point. The sign of $G$ depends on the coefficients in the renormalization-group $\beta$ function.

The entropy of a Robertson-Walker universe ($k=1\mathrm{}$, $\Lambda >0\mathrm{}$) in statistical thermodynamic stable equilibrium with conformal bosons is calculated with use of a new self-consistent method. Its value is similar to but higher than the entropy of an alternative empty de Sitter solution, which may help in interpretation of Hawking thermal states.

By exploitation of the overcompleteness of coherent states expressions are presented for path integrals in terms of genuine (Wiener) path-space measures for driven harmonic oscillators which when projected onto the subspace spanned by coherent-state matrix elements yield the appropriate quantum mechanical propagator.

The universal Newtonian gravitational constant is being redetermined at the National Bureau of Standards with use of the method of Boyes in which the period of a torsion pendulum is altered by the presence of two 10.5-kg tungsten balls. The difference in the squares of the frequencies with and without the balls is proportional to $G$. The resulting value of $G$ is (6.6726±0.0005)×${10}^{-11\mathrm{}}$ ${\mathrm{m}}^3$· ${\sec }^{-2\mathrm{}}$· ${\mathrm{kg}}^{-1\mathrm{}}$·

The transmission coefficient for passage through a barrier with a parabolic maximum is computed rigorously when linear passive dissipation is present. The exact result for energies above and below the barrier height can be expressed in terms of the Coleman renormalized one-bounce time. The quasiclassical (WKB) approximation is recovered for energies significantly below the barrier height where "friction" enhances the tunneling probability.

The fine-structure constant $\alpha$ has been determined from precision measurements of quantized Hall resistances $R_{\mathrm{H}}$ of three different GaAs-${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructures. The result, ${\alpha }^{-1\mathrm{}}=137.035\mathrm{}968\left(23\right)\mathrm{}$ (0.17 ppm), is in excellent agreement with the 0.11-ppm value obtained from the gyromagnetic ratio of the proton, ${{\gamma }_p}^{\prime }$, and $\frac{2e}{h}$ via the Josephson effect. Our $R_{\mathrm{H}}$ value can be combined with ${{\gamma }_p}^{\prime }$ and $\frac{2e}{h}$ to yield a more accurate value of ${\alpha }^{-1\mathrm{}}$ independent of the ohm: ${\alpha }^{-1\mathrm{}}=137.035\mathrm{}965\left(12\right)\mathrm{}$ (0.089 ppm).

A new type of universality associated with the onset of a deterministic diffusion for systems described by iterative one-dimensional maps is reported. The diffusion coefficient $D$ plays the role of an order parameter with a universal critical exponent. For the presence of external noise, the existence of a universal scaling function $d$ is shown. An analytic expression is derived for $d$ which is in good agreement with results of a numerical experiment.

The London equations, which were proposed as restrictions to conventional classical electromagnetism in order to explain the Meissner-Ochsenfeld effect in superconductors, are derived from familiar classical action integrals. The equations of motion, from which the London equations follow, should apply to some collisionless plasmas. Space and thermonuclear applications are timely and significant.

$\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}\otimes \mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ spin systems in two dimensions are studied for $N=2, 3, \mathrm{and} 4$ on 10×10, 20×20, and 30×30 lattices with use of Monte Carlo methods. Variant forms of the action are considered. In addition to crossover phenomena, unexpected first-order transitions in multidimensional phase diagrams are discovered. These transitions are related to the presence of $Z_N$ vortices which experience short-range interactions. Contrasts with $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ gauge theories in four dimensions are drawn.

A nontrivial family of $d$-dimensional scale-invariant fractal lattices is described, on which statistical mechanics and conductivity problems are exactly solvable for every $d$. These fractals are finitely ramified but not quasi one dimensional, and hence can be used to model the important geometrical features of the percolating cluster's backbone. Critical exponents calculated for this model agree with those of "real" systems at low dimensionalities.

A new double Penning trap structure has been built which permits one to trap a positron in a well-compensated experiment trap where measurements have yielded the geonium positron $g$-factor anomaly, $\frac{g\left(e^{+}\right)}{2}-1\mathrm{}\equiv a\left(e^{+}\right)=(1\mathrm{}159652222\pm 50)\times {10}^{-12\mathrm{}}$. The uncertainty is based on the resonance linewidths and an estimate of the remaining systematic error associated with extrapolating to zero spin-flip power. By comparison to the electron-spin anomaly, a positron/electron $g$-factor ratio of 1 + (22±64)×${10}^{-12\mathrm{}}$ is obtained.

In problems involving two-dimensional area-preserving maps, stochastic regions are separated by continuous curves called Kolmogorov-Arnold-Moser trajectories. As the mapping is changed continuously, these regions may fuse via the disappearance of the intervening trajectories. Scaling arguments are presented to describe the behavior of the curves near their disappearance.

The $L\to \infty$ asymptotic properties of ${\rho }_L\mathrm{}\left(g\right)\mathrm{}$, the probability distribution of the classical hopping conductivity $g_L$ corresponding to random one-dimensional systems of length $L$, are determined. These properties are nonuniversal, and become anomalous if the probability density $\rho \mathrm{}\left(w\right)\mathrm{}$ of the random near-neighbor hopping rates is such that $\int 0^{\infty }\mathrm{dw}\rho \mathrm{}\left(w\right)\mathrm{}{w}^{-1\mathrm{}}$ does not exist. The associated quasilocalization effects are discussed and their experimental observability is speculated upon.