321 research outputs found
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
Ground State and Excitations of Quantum Dots with "Magnetic Impurities"
We consider an "impurity" with a spin degree of freedom coupled to a finite
reservoir of non-interacting electrons, a system which may be realized by
either a true impurity in a metallic nano-particle or a small quantum dot
coupled to a large one. We show how the physics of such a spin impurity is
revealed in the many-body spectrum of the entire finite-size system; in
particular, the evolution of the spectrum with the strength of the
impurity-reservoir coupling reflects the fundamental many-body correlations
present. Explicit calculation in the strong and weak coupling limits shows that
the spectrum and its evolution are sensitive to the nature of the impurity and
the parity of electrons in the reservoir. The effect of the finite size
spectrum on two experimental observables is considered. First, we propose an
experimental setup in which the spectrum may be conveniently measured using
tunneling spectroscopy. A rate equation calculation of the differential
conductance suggests how the many-body spectral features may be observed.
Second, the finite-temperature magnetic susceptibility is presented, both the
impurity susceptibility and the local susceptibility. Extensive quantum
Monte-Carlo calculations show that the local susceptibility deviates from its
bulk scaling form. Nevertheless, for special assumptions about the reservoir --
the "clean Kondo box" model -- we demonstrate that finite-size scaling is
recovered. Explicit numerical evaluations of these scaling functions are given,
both for even and odd parity and for the canonical and grand-canonical
ensembles.Comment: 16 pages; published version, corrections to figure and equation,
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
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