1,069 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
Weak-Localization in Chaotic Versus Non-Chaotic Cavities: A Striking Difference in the Line Shape
We report experimental evidence that chaotic and non-chaotic scattering
through ballistic cavities display distinct signatures in quantum transport. In
the case of non-chaotic cavities, we observe a linear decrease in the average
resistance with magnetic field which contrasts markedly with a Lorentzian
behavior for a chaotic cavity. This difference in line-shape of the
weak-localization peak is related to the differing distribution of areas
enclosed by electron trajectories. In addition, periodic oscillations are
observed which are probably associated with the Aharonov-Bohm effect through a
periodic orbit within the cavities.Comment: 4 pages revtex + 4 figures on request; amc.hub.94.
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
On the Inequivalence of Weak-Localization and Coherent Backscattering
We define a current-conserving approximation for the local conductivity
tensor of a disordered system which includes the effects of weak localization.
Using this approximation we show that the weak localization effect in
conductance is not obtained simply from the diagram corresponding to the
coherent back-scattering peak observed in optical experiments. Other diagrams
contribute to the effect at the same order and decrease its value. These
diagrams appear to have no semiclassical analogues, a fact which may have
implications for the semiclassical theory of chaotic systems. The effects of
discrete symmetries on weak localization in disordered conductors is evaluated
and and compared to results from chaotic scatterers.Comment: 24 pages revtex + 12 figures on request; hub.94.
Quantum mechanics on a circle: Husimi phase space distributions and semiclassical coherent state propagators
We discuss some basic tools for an analysis of one-dimensionalquantum systems
defined on a cyclic coordinate space. The basic features of the generalized
coherent states, the complexifier coherent states are reviewed. These states
are then used to define the corresponding (quasi)densities in phase space. The
properties of these generalized Husimi distributions are discussed, in
particular their zeros.Furthermore, the use of the complexifier coherent states
for a semiclassical analysis is demonstrated by deriving a semiclassical
coherent state propagator in phase space.Comment: 29 page
Incipient Wigner Localization in Circular Quantum Dots
We study the development of electron-electron correlations in circular
quantum dots as the density is decreased. We consider a wide range of both
electron number, N<=20, and electron gas parameter, r_s<18, using the diffusion
quantum Monte Carlo technique. Features associated with correlation appear to
develop very differently in quantum dots than in bulk. The main reason is that
translational symmetry is necessarily broken in a dot, leading to density
modulation and inhomogeneity. Electron-electron interactions act to enhance
this modulation ultimately leading to localization. This process appears to be
completely smooth and occurs over a wide range of density. Thus there is a
broad regime of ``incipient'' Wigner crystallization in these quantum dots. Our
specific conclusions are: (i) The density develops sharp rings while the pair
density shows both radial and angular inhomogeneity. (ii) The spin of the
ground state is consistent with Hund's (first) rule throughout our entire range
of r_s for all 4<N<20. (iii) The addition energy curve first becomes smoother
as interactions strengthen -- the mesoscopic fluctuations are damped by
correlation -- and then starts to show features characteristic of the classical
addition energy. (iv) Localization effects are stronger for a smaller number of
electrons. (v) Finally, the gap to certain spin excitations becomes small at
the strong interaction (large r_s) side of our regime.Comment: 14 pages, 12 figure
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
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