Sorting on a ring of processors

We study the time necessary to sort on a ring of processors. We show that the amount of space available to each processor determines the time required. We prove a lower bound of 2[n/2] − 1 steps for sorting on a ring of n processors, under the constraint that each processor retains only a single value at any time. In contrast, we show an algorithm that sorts in [n/2] + 1 steps if each processor is allowed to store six values.     

Silicon as a standard material for infrared reflectance and transmittance from 2 to 5 μm

We have investigated the specular reflectance and transmittance of polished, high-resistivity single-crystal Si in the spectral range from 2 to 5 μm. Measurements were performed with a nearly collimated (≈0.7° divergence) beam at angles of incidence from 12° to 80°, and a spectral resolution of 16 cm⁻¹. The measured values agree with the expected values obtained from the published index of refraction of Si to within 0.002. This represents a substantial reduction in experimental uncertainty compared to previous results and demonstrates the usefulness of Si as a standard material for infrared reflectance and transmittance.     

Convergence of U(1)3 lattice gauge theory to its continuum limit

It is shown that in three space-time dimensions the pure U(1) lattice gauge theory with Villain action and fixed coupling constant converges to the free electromagnetic field as the lattice spacing approaches zero. The same holds for the Wilson action on the electric sector.     

The atom as a probe of curved space-time

A one-electron atom is considered in a general curved space-time. The Hamiltonian of the Dirac equation is written in Fermi normal coordinates, including all interaction terms of first order in the Riemann tensor of the space-time. Expressions are obtained for the shifts in various atomic energy levels caused by the curvature. There is a possibility that these shifts would be observable in the spectrum of hydrogen falling into small black holes (radius about 10^–3 cm) left over from the early universe.This essay received the fifth award from the Gravity Research Foundation for the year 1980.-Ed.Work supported in part by the National Science Foundation.     

Gravitons from anomalous decay

The decay rate of the neutral pion into two gravitons is calculated from the gravitational anomaly in the axial current. Although this decay rate is negligible relative to the decay rate of the neutral pion into two photons, the rate of decay into gravitons is proportional to the seventh power of the mass of the decaying particle, and to the square of the gravitational constant. The possibility that a particle of very large mass, associated with an axial current anomaly, was present in the early universe is considered. Such a particle would decay at a significant rate into gravitons. As these gravitons would not be thermaiized, they would result in a (potentially observable) nonthermal spectrum of gravitational waves present today. The peak frequency of this gravitational wave spectrum would be indicative of the mass of the decaying particle. Alternatively, if the gravitational constant were large at early times, then the gravitational decay of the pion would be significant in the early universe, giving rise to a nonthermal gravitational wave spectrum.