We develop a statistical theory describing quantum-mechanical scattering of a particle by a cavity when the geometry is such that the classical dynamics is chaotic. This picture is relevant to a variety of physical systems, ranging from atomic nuclei to mesoscopic systems and microwave cavities; the main application here is to electronic transport through ballistic microstructures. The theory describes the regime in which there are two distinct timescales, associated with a prompt and an equilibrated response, and is cast in terms of the matrix of scattering amplitudes S. The prompt response is related to the energy average of S which, through the notion of ergodicity, is expressed as the average over an ensemble of similar systems. We use an information-theoretic approach: the ensemble of S matrices is determined by (1) general physical features, such as symmetry, causality, and ergodicity, (2) the specific energy average of S, and (3) the notion of minimum information in the ensemble. This ensemble, known as Poisson's kernel, is meant to describe those situations in which any other information is irrelevant. Thus, one constructs the one-energy statistical distribution of S using only information expressible in terms of S itself, without ever invoking the underlying Hamiltonian. This formulation has a remarkable predictive power: from the distribution of S we derive properties of the quantum conductance of cavities, including its average, its fluctuations, and its full distribution in certain cases, both in the absence and in the presence of prompt response. We obtain good agreement with the results of the numerical solution of the Schrödinger equation for cavities in which the assumptions of the theory hold, namely, cavities in which either prompt response is absent or there are two widely separated timescales. Good agreement with experimental data is obtained once temperature-smearing and dephasing effects are taken into account.
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Document Type: Miscellaneous
Instituto de Física, Universidad Nacional Autónoma de México, 01000 México DF, Mexico
Bell Laboratories - Lucent Technologies, 700 Mountain Avenue 1D-230, Murray Hill, NJ 07974, USA
Publication date: February 1, 1999