Interference Phenomena in Electronic Transport Through Chaotic Cavities An Information-Theo.pdfVIP

a r X i v : c o n d - m a t / 9 8 1 2 2 2 5 v 1 [ c o n d - m a t .m e s - h a l l ] 1 4 D e c 1 9 9 8 Interference Phenomena in Electronic Transport Through Chaotic Cavities: An Information-Theoretic Approach Pier A. Mello? and Harold U. Baranger? ? Instituto de F??sica, Universidad Nacional Auto?noma de Me?xico, 01000 Me?xico D.F., Me?xico ? Bell Laboratories– Lucent Technologies, 700 Mountain Ave. 1D-230, Murray Hill NJ 07974 1 December 1998 Abstract. 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 to microwave cavities; the main application here is to electronic transport through ballistic microstructures. The theory describes the regime in which there are two distinct time scales, 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– 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 abse