An exact, asymptotically flat, stationary solution of the field equations of O(2) extended supergravity theory is presented. This solution has a mass, central electric charge as well as a supercharge, and constitutes the first exact, supersymmetric generalization of the black-hole geometries. The solution generalizes the extreme Reissner-Nordström black holes.

It is shown that electromagnetic and clock-transport synchronization procedures are not necessarily equivalent. In noninertial frames and in gravitational fields both procedures can be path dependent. Even for the same path ∼ 100 km above the Earth, the two procedures can give different errors, ∼ 89 μsec/day (clock-transport synchronization) and ∼ 60 μsec/day (electromagnetic synchronization).

It is shown that for hard-sphere systems in a constant external potential revised Enskog theory yields the correct single-particle equilibrium distribution function, whereas standard Enskog theory does not.

The motion of a quantum mechanical particle is studied in the presence of a periodic potential and frictional forces. Depending on the parameters, the behavior changes from diffusion to localization.

Upper and lower bounds are obtained for the potential energy of two-dimensional classical systems consisting of particles interacting via a short-range potential that has a hard-disk core. The bounds coincide in the close-packing limit, implying that first-order thermodynamic perturbation theory becomes exact in this limit.

Neutron interferometry has been performed on an accelerated interferometer under conditions where gravitational effects on the interfering beams very nearly compensate each other. The observed neutron phase shift is found to be in excellent agreement with that calculated from Schrödinger's equation transformed to the accelerated frame where it is found essential to include the spherical wave aspect. The present experiment thus verifies the validity of the classical transformation laws for noninertial frames also in the quantum limit.

A solution is given to the problem of finding the continuous quantum nondemolition observables of a given system which has a classical analog. It is found that there are a nondenumerably infinite number of such observables which are generated by an arbitrary function. As an example the "mass on a negative spring" case is solved for a particular choice of the function.

The authors show how to construct a normalizable resonance wave function produced by a sharp-cutoff two-body potential using analyticity and basic quantum mechanical requirements. To this end they propose a saturation scheme, and estimate the duration of validity of the exponential decay law. The viability of the model is tested in a deuteron stripping to unbound-state calculation.

A fluid flows parallel to the strata of an $n$-layer stratified system. Particles suspended in the fluid are carried along with the flow, and additionally make random jumps into neighboring strata, where the flow velocity is different. The spatial dispersion of the particles in the flow direction, for long times, is calculated exactly for arbitrary $n$, jump rates, and velocity field. The result is applied to a variety of phenomena, e.g., chromatography, Taylor diffusion, and random walks.

An exact solution of the Einstein equations in vacuum representing two pairs of gravitational solitons propagating on an expanding universe is given and studied. It is suggested that the solitons evolve from quasiparticles to pure gravitational waves. Two of the four solitons collide and the focusing produced on null rays is studied. Although the spacetime following the collision is highly distorted, null rays do not focus to a singularity.

A model of interacting random walks is proposed in which each new site visited has a weight factor $p$. For $1<~p<~\infty$, the model interpolates between purely random walks and self-avoiding walks. When $0<p<\mathrm{}1\mathrm{}$, the model describes attracting random walks (and also noninteracting random walks on a lattice with static traps), and shares some of the intriguing features of random walks on percolation fractals—e.g, dimension-independent exponents.

For Hermitian many-body systems, admissible functions for the velocity autocorrelation function form a certain invariant of time. This property originates from a basic recurrence relation. The exponentially decaying function cannot form an invariant and therefore cannot be admissible.

A general class of models is introduced which relate the motion of a phase boundary to properties of the local interfacial geometry. These systems can undergo successive destabilizations as they grow, possibly giving rise to nonequilibrium spatial patterns. This formalism has applications to a wide variety of physical problems, especially including dendritic solidification.

Unrestricted lattice random walks in which a unit conductor is placed along each bond traversed are considered. The mean end-to-end resistance is studied as a function of the number of steps in the walk and the spatial dimension. A critical scaling law is found whose exponent is consistently given by four different calculational schemes.

A model for diffusion-controlled aggregation in which growing clusters as well as individual particles are mobile has been investigated. Two versions of the model in which the cluster diffusion coefficient is either size independent or inversely proportional to number of particles (mass) give very similar results. In the limit of low concentration and large system size both models lead to structures with a fractal (Hausdorff) dimensionality of about 1.45-1.5 in two-dimensional lattice-based simulations.

A model describing the process of cluster growth by aggregation of clusters is introduced and investigated with the Monte Carlo method. It is found that the clusters are scale invariant. The fractal dimension of this new class of kinetic critical behavior is $D={\nu }^{-1\mathrm{}}=1.38\mathrm{}\pm 0.06$ in $d=2\mathrm{}$ dimensions as determined by the radii of gyration and the density correlations of the aggregates. The process is compared with other types of kinetic and equilibrium critical phenomena.

New expressions for the availability dissipated in a finite-time endoreversible process are found by use of Weinhold's metric on equilibrium states of a thermodynamic system. In particular, the dissipated availability is given by the square of the length of the corresponding curve, times a mean relaxation time, divided by the total time of the process. The results extend to local thermodynamic equilibrium if instead of length one uses distance (length of the shortest curve) between initial and final states.

Inverting the spin state of one of the two coherent waves propagating within a neutron interferometer by means of a radio-frequency spin-flip device leads to a nonstationary interference pattern. By using stroboscopic neutron detection one can resolve this to demonstrate the nonclassical behavior of spinor superposition.

The evolution of the orbit of a binary pulsar under the action of gravitational radiation reaction is calculated. No approximation is made of weak gravity inside the individual stars; the details of the orbital motion are given directly (to order $c^{-5\mathrm{}}$ and $G^3$). The calculation reveals no acceleration of the center of mass of the system, and a secular decrease of the time of return to periastron. The quantitative results agree both with the well-known "quadrupole formula" and with observations.

The distribution of energy eigenvalues in the irregular spectrum is derived in the semiclassical limit $\hslash \to 0$ by use of a plausible assumption on the spatial distribution of the corresponding eigenfunctions.