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 dynamics is chaotic. This picture is relevant to a variety of systems, ranging from atomic nuclei 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 ergodicity, is expressed as the average over an ensemble of 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 absence and presence prompt response. We obtain good agreement with the results of the numerical solution of the Schrodinger equation for cavities in which either prompt response is absent or there are two widely separated time scales. Good agreement with experimental data is obtained once temperature smearing and dephasing effects are taken into account.Comment: 38 pages, 11 ps files included, uses IOP style files and epsf.st

Localization in an Inhomogeneous Quantum Wire

We study interaction-induced localization of electrons in an inhomogeneous quasi-one-dimensional system--a wire with two regions, one at low density and the other high. Quantum Monte Carlo techniques are used to treat the strong Coulomb interactions in the low density region, where localization of electrons occurs. The nature of the transition from high to low density depends on the density gradient--if it is steep, a barrier develops between the two regions, causing Coulomb blockade effects. Ferromagnetic spin polarization does not appear for any parameters studied. The picture emerging here is in good agreement with measurements of tunneling between two wires.Comment: 4 pages; 2 new figures, substantial revisions and clarification

Reflection Symmetric Ballistic Microstructures: Quantum Transport Properties

We show that reflection symmetry has a strong influence on quantum transport properties. Using a random S-matrix theory approach, we derive the weak-localization correction, the magnitude of the conductance fluctuations, and the distribution of the conductance for three classes of reflection symmetry relevant for experimental ballistic microstructures. The S-matrix ensembles used fall within the general classification scheme introduced by Dyson, but because the conductance couples blocks of the S-matrix of different parity, the resulting conductance properties are highly non-trivial.Comment: 4 pages, includes 3 postscript figs, uses revte

Chaos and Interacting Electrons in Ballistic Quantum Dots

We show that the classical dynamics of independent particles can determine the quantum properties of interacting electrons in the ballistic regime. This connection is established using diagrammatic perturbation theory and semiclassical finite-temperature Green functions. Specifically, the orbital magnetism is greatly enhanced over the Landau susceptibility by the combined effects of interactions and finite size. The presence of families of periodic orbits in regular systems makes their susceptibility parametrically larger than that of chaotic systems, a difference which emerges from correlation terms.Comment: 4 pages, revtex, includes 3 postscript fig

Semiclassical Approach to Orbital Magnetism of Interacting Diffusive Quantum Systems

We study interaction effects on the orbital magnetism of diffusive mesoscopic quantum systems. By combining many-body perturbation theory with semiclassical techniques, we show that the interaction contribution to the ensemble averaged quantum thermodynamic potential can be reduced to an essentially classical operator. We compute the magnetic response of disordered rings and dots for diffusive classical dynamics. Our semiclassical approach reproduces the results of previous diagrammatic quantum calculations.Comment: 8 pages, revtex, includes 1 postscript fi