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The conductance of a sample scattering elastically and coupled to leads with many channels is derived. We assume that all the incident channels on one side of the sample are fed from the same chemical potential. The transmitted and reflected streams are determined by the incident streams through the multichannel scattering properties of the sample. We do not assume that the channels equilibrate with each other. Our result differs from those given earlier by other authors, except for that of Azbel [J. Phys. C 14, L225 (1981)],which is confirmed. We point out that a similar result is obtained for the conductance in a single channel at a temperature above zero. As an application, we obtain the dependence on channel number N of the contributions to the conductance of a small ring, periodic in the Aharonov-Bohm flux through it. Terms whose period is h/e as well as those with period h /2e vary with X as 1/X.

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The existing theories of the resistivity of mixtures assume regular arrangements of the two components, rather than random mixtures. A theory for a random mixture is given, based on the assumption that each crystal acts as if surrounded by a homogeneous medium whose properties are those of the mixture. Comparisons with experiment are made. The experimental data that have been examined fall roughly into two classes. One class consists of mixtures, where the variation of resistivity with composition disagrees violently with this theory, making it clear that the assumptions made are completely inapplicable. The remaining class consists of mixtures which generally agree well with the theory.

This section, offered as an experiment beginning in January 1992, contains short articles intended to describe recent research of interest to a broad audience of physicsts. It will concentrate on research at the frontiers of physics, especially on concepts able to link many different subfields of physics. Responsibility for its contents and readability rests with the Advisory Committee on Colloquia, U. Fano, chair, Robert Cahn, S. Freedman, P. Parker, C. J. Pethick, and D. L. Stein. Prospective authors are encouraged to communicate with Professor Fano or one of the members of this committee.Over sixty years ago, it was suggested that there is a time associated with the passage of a particle under a tunneling barrier. The existence of such a time is now well accepted; in fact the time has been measured experimentally. There is no clear consensus, however, about the existence of a simple expression for this time, and the exact nature of that expression. The proposed expressions fall into three main classes. The authors argue that expressions based on following a feature of a wave packet through the barrier have little physical significance. A second class tries to identify a set of classical paths associated with the quantum-mechanical motion and then tries to average over these. This class is too diverse to permit assessment as a single entity. The third class invokes a physical clock involving degrees of freedom in addition to that involved in tunneling. This not only is a prescription for the derivation of expressions for the traversal time but also leads to a direct relationship to experiment.