We develop a statistical theory describing quantum-mechanical scattering of aparticle by a cavity when the geometry is such that the classical dynamics ischaotic. This picture is relevant to a variety of systems, ranging from atomicnuclei to microwave cavities; the main application here is to electronictransport through ballistic microstructures. The theory describes the regime inwhich there are two distinct time scales, associated with a prompt and anequilibrated response, and is cast in terms of the matrix of scatteringamplitudes S. The prompt response is related to the energy average of S which,through ergodicity, is expressed as the average over an ensemble of systems. Weuse an information-theoretic approach: the ensemble of S-matrices is determinedby (1) general physical features-- symmetry, causality, and ergodicity, (2) thespecific energy average of S, and (3) the notion of minimum information in theensemble. This ensemble, known as Poisson's kernel, is meant to describe thosesituations in which any other information is irrelevant. Thus, one constructsthe one-energy statistical distribution of S using only information expressiblein terms of S itself without ever invoking the underlying Hamiltonian. Thisformulation has a remarkable predictive power: from the distribution of S wederive properties of the quantum conductance of cavities, including itsaverage, its fluctuations, and its full distribution in certain cases, both inthe absence and presence prompt response. We obtain good agreement with theresults of the numerical solution of the Schrodinger equation for cavities inwhich either prompt response is absent or there are two widely separated timescales. Good agreement with experimental data is obtained once temperaturesmearing and dephasing effects are taken into account.
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