Quantum Scattering and Transport inClassically Chaotic Cavities: An Overview ofOld and New Results

摘要

We develop a statistical theory that describes 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, rang- ing from atomic nuclei to mesoscopic systems and microwave cavities: the main application to be discussed in this contribution is the electronic transport through mesoscopic ballistic structures or quantum dots. The theory describes the regime in which there are two distinct time scales, associated with a prompt and an equili-brated response, and is cast in terms of the matrix of scattering amplitudes S. We construct the ensemble of S matrices using a maximum-entropy approach which incorporates the requirements of flux conservation, causality and ergodicity, and the system-specific average of S which quantifies the effect of prompt processes. The resulting ensemble, known as Poisson's kernel, is meant to describe those situ-ations in which any other information is irrelevant. The results of this formulation have been compared with the numerical solution of the Schrodinger equation for cavities in which the assumptions of the theory hold. The model has a remarkable predictive power: it describes statistical properties of the quantum conductance of quantum dots, like its average, its fluctuations, and its full distribution in several cases. We also discuss situations that, have been found recently, in which the notion of st ationarity and ergodicity is not fulfilled, and yet Poisson's kernel gives a good description of the data. At the present moment we are unable to give an explana-tion of this tact.