Interference phenomena in electronic transport through chaotic cavities: an information-theoretic approach

We develop a statistical theory describing quantum-mechanical scattering of a particle by a cavity when the geometry is such that the classical dynami cs is chaotic. This picture is relevant to a variety of physical systems, r anging from atomic nuclei to mesoscopic systems and microwave cavities; the main application here is to electronic transport through ballistic microst ructures. The theory describes the regime in which there are two distinct t imescales, associated with a prompt and an equilibrated response, and is ca st in terms of the matrix of scattering amplitudes S. The prompt response i s related to the energy average of S which, through the notion of ergodicit y, 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 ergodic ity, (2) the specific energy average of S, and (3) the notion of minimum in formation in the ensemble. This ensemble, known as Poisson's kernel, is mea nt to describe those situations in which any other information is irrelevan t. Thus, one constructs the one-energy statistical distribution of S using only information expressible in terms of S itself, without ever invoking th e underlying Hamiltonian. This formulation has a remarkable predictive powe r: from the distribution of S we derive properties of the quantum conductan ce of cavities, including its average, its fluctuations, and its full distr ibution in certain cases, both in the absence and in the presence of prompt response. We obtain good agreement with the results of the numerical solut ion of the Schrodinger equation for cavities in which the assumptions of th e theory hold, namely, cavities in which either prompt response is absent o r there are two widely separated timescales. Good agreement with experiment al data is obtained once temperature-smearing and dephasing effects are tak en into account.