It is shown that a trapped surface can be extended, in a locally area-preserving fashion, to a three-cylinder that is everywhere spacelike, provided it encounters no singularities in its development. Thus the interior of a regular, area-preserving, initially trapped surface is permanently sealed off from causal influence on the exterior world.

Evidence for the Aharonov-Bohm effect was obtained with magnetic fields shielded from the electron wave. A toroidal ferromagnet was covered with a superconductor layer to confine the field, and further with a copper layer for complete shielding from the electron wave. The expected relative phase shift was detected with electron holography between two electron beams, one passing through the hole of the toroid, and the other passing outside. The experiment gave direct evidence for flux quantization also.

It is shown that the localization length of quasienergy eigenfunctions is determined by the classical diffusion rate: l=D/2. The new numerical method of minimal Lyapunov exponent for the calculation of l is proposed and applied to the quantum standard map and Lloyd model.

We have found quantum chaos in a system consisting of two levels coupled through a time-dependent perturbation, when this perturbation is quasiperiodic with two incommensurate frequencies. This contrasts with the case of a monochromatic perturbation where the oscillations of the physical observables are nonchaotic, because of the Floquet theorem. The existence of chaos is confirmed by the observation of rapidly decreasing autocorrelation functions, and by a continuous Fourier spectrum for time-dependent fluctuations of physical observables.

The limiting distribution P(s) of quasienergy-level spacings is investigated for a quantum model which is stochastic in the classical limit. The numerical results show that in the case of a strong perturbation, the distribution P(s) corresponds closely to the Wigner-Dyson distribution. The relations between the limiting distribution P(s) and the symmetries of both the unperturbed and perturbed motions are independently investigated.

The formula for the fractal dimensionality of the perimeter (hull) of a percolation cluster, ${\mathrm{d}}_{\mathrm{f}}^{\mathcal{’}}$=1+1/ν, proposed recently by Sapoval, Rosso, and Gouyet, is shown to imply for the perimeter scaling exponents τ’=1+2ν/(1+ν), σ’=1/(1+ν), and γ’=2. Monte Carlo simulations of very large perimeter-generating walks yield τ’=2.143±0.002 and ${\mathrm{d}}_{\mathrm{f}}^{\mathcal{’}}$=1.751±0.002, consistent with these predictions (on the assumption that ν=(4/3)). The walks are also used to determine ${\mathrm{p}}_{\mathrm{c}}$=0.5927 5±0.0000 3 for site percolation on a square lattice.

We present analytic properties of the power spectrum for a class of chaotic dynamical systems (Axiom-A systems). The power spectrum is meromorphic in a strip; the position of the poles (resonances) depends on the system considered, but only their residues depend on the observable monitored. In relation with these results we also discuss the exponential or nonexponential decay of correlation functions at infinity. In conclusion, it appears desirable to analyze the decay of correlation functions and the possible analyticity of power spectra for physical time evolutions, and for computer generated simple dynamical systems (non-Axiom-A in general).

We argue that the mass gap in the O(3) σ model is produced by condensation of vortices of topological charge (1/2) (merons). This mechanism is not effective at topological angle theta=π, supporting arguments that this model is massless. These two models are the large-spin limit of integer (half-integer) quantum spin chains.

We present a new approach for calculations of the electronic structure of atoms and molecules. The main features are (1) a functional-integral formulation on a lattice in space and imaginary time, (2) renormalization-group transformations which increase lattice spacings to reduce the number of degrees of freedom, (3) perturbation-theory treatments of core electrons, and (4) a Monte Carlo technique using the Langevin equation for nonpertubative calculations of valence-electron properties at low temperatures.

A simple scaling description of the ordering transition in random-field Ising systems is developed and supported by renormalization-group arguments in terms of a zero-temperature critical fixed point. The main prediction is that the characteristic relaxation time τ will diverge extremely rapidly as the critical point is approached: τ∼exp(${\xi }^{\mathrm{theta}}$) with ξ the correlation length and theta the ‘‘violation of hyperscaling’’ exponent (d-theta)ν=2-α. Recent experiments which exhibit onset of hysteresis in a very narrow temperature range are discussed.

A theory of quantum tunneling with dissipation is constructed. The frequency-dependent transmission coefficient is calculated at zero and finite temperatures. A fluctuation-dissipation theorem for tunneling particles is derived.

We discuss the conditions that dynamic symmetries impose on the scattering S matrices and construct these matrices for problems with SO(2,1), SO(2,2), and SO(2,3) dynamical groups. The latter group appears to be very useful for the analysis of heavy-ion collisions.

The route to chaos found from the delay-differential rate equations is basically different from the subharmonic cascade which is generic of the adiabatic-following-approximation equation. The Lyapunov dimension of each chaotic attractor is found to increase linearly with γ${\mathrm{\tau }}_{\mathrm{R}}$, the ratio of the delay time to the medium lifetime. This clearly shows the invalidity of the difference-equation mapping whose dimension never exceeds 2.

We describe a new method of measuring the Lense-Thirring relativistic nodal drag using LAGEOS together with another high-altitude, laser-ranged, similar satellite with appropriately chosen orbital parameters. We propose, for this purpose, that a future satellite such as LAGEOS II have an inclination supplementary to that of LAGEOS. The experiment proposed here would provide a method for experimental verification of the general relativistic formulation of Mach’s principle and measurement of the gravitomagnetic field.

We used the relativistic Doppler effect to shift the energy of the fourth-harmonic photons of a Nd-doped yttrium aluminum garnet laser into the range from 1.4 to 15.8 eV in a moving atom’s reference frame by varying the angle of intersection theta between the laser beam and an 800-MeV atomic hydrogen (${\mathrm{H}}^0$) beam. We measured the intersection angle theta for several well known Lyman transitions (1s to np) in ${\mathrm{H}}^0$ and fitted these data by the form E=($E_0$/$g_0$)γ(1+β costheta). The value of $E_0$/$g_0$ obtained in this manner, compared with the measured value of $E_0$ for the laser photons, yielded $g_0$=1.000 04(27) at β≃0.84. The prediction of special relativity that $g_0$=1 is thus verified to an accuracy of 2.7×${10}^4$.

A two-level system is treated which interacts with a degenerate fermionic heat bath. Arbitrarily strong screening by fermions is taken into account. The hopping of the two-level system may be spontaneous or assisted by the fermionic bath. By derivation of scaling equations it is shown for the spin-(1/2) case that because of the assisted hops the two-level system cannot be localized in one of the states.

We consider the problem of a free particle in a rigid box with one wall fixed and the other oscillating periodically in time. The spectral properties of the evolution operator are calculated. We find that by a tuning of Planck’s constant, the statistics of the quasienergy spectrum go continuously from showing Poisson to Gaussian-orthogonal-ensemble-like properties. This change is related to a transition from localized to extended states in energy space. We make the conjecture that recent results of microwave excitations on quasi one-dimensional highly excited hydrogen atoms may be related to this work.

Consequences of geometrical constraints from integrability along all super lightlike lines are examined in N-extended supergravity theories. It is shown that these constraints give rise, through Bianchi identities, to equations of motion of the conformal type for all forms of physical fields, with N>4. Our results point to an integrability program for N>4 supergravity similar to that for N>2 supersymmetric Yang-Mills fields.

Expressions are derived for the expected abundance of clusters and voids in a sample of randomly distributed objects.

We have carefully reexamined the results of the experiment of Eötvös, Pekár, and Fekete, which compared the accelerations of various materials to the Earth. We find that the Eötvös-Pekár-Fekete data are sensitive to the composition of the materials used, and that their results support the existence of an intermediate-range coupling to baryon number or hypercharge.