10,523 research outputs found
Statistical study of the conductance and shot noise in open quantum-chaotic cavities: Contribution from whispering gallery modes
In the past, a maximum-entropy model was introduced and applied to the study
of statistical scattering by chaotic cavities, when short paths may play an
important role in the scattering process. In particular, the validity of the
model was investigated in relation with the statistical properties of the
conductance in open chaotic cavities. In this article we investigate further
the validity of the maximum-entropy model, by comparing the theoretical
predictions with the results of computer simulations, in which the Schroedinger
equation is solved numerically inside the cavity for one and two open channels
in the leads; we analyze, in addition to the conductance, the zero-frequency
limit of the shot-noise power spectrum. We also obtain theoretical results for
the ensemble average of this last quantity, for the orthogonal and unitary
cases of the circular ensemble and an arbitrary number of channels. Generally
speaking, the agreement between theory and numerics is good. In some of the
cavities that we study, short paths consist of whispering gallery modes, which
were excluded in previous studies. These cavities turn out to be all the more
interesting, as it is in relation with them that we found certain systematic
discrepancies in the comparison with theory. We give evidence that it is the
lack of stationarity inside the energy interval that is analyzed, and hence the
lack of ergodicity that gives rise to the discrepancies. Indeed, the agreement
between theory and numerical simulations is improved when the energy interval
is reduced to a point and the statistics is then collected over an ensemble. It
thus appears that the maximum-entropy model is valid beyond the domain where it
was originally derived. An understanding of this situation is still lacking at
the present moment.Comment: Revised version, minor modifications, 28 pages, 7 figure
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
Wave Scattering through Classically Chaotic Cavities in the Presence of Absorption: An Information-Theoretic Model
We propose an information-theoretic model for the transport of waves through
a chaotic cavity in the presence of absorption. The entropy of the S-matrix
statistical distribution is maximized, with the constraint : n is the dimensionality of S, and meaning complete (no) absorption. For strong absorption our result
agrees with a number of analytical calculations already given in the
literature. In that limit, the distribution of the individual (angular)
transmission and reflection coefficients becomes exponential -Rayleigh
statistics- even for n=1. For Rayleigh statistics is attained even
with no absorption; here we extend the study to . The model is
compared with random-matrix-theory numerical simulations: it describes the
problem very well for strong absorption, but fails for moderate and weak
absorptions. Thus, in the latter regime, some important physical constraint is
missing in the construction of the model.Comment: 4 pages, latex, 3 ps figure
Statistical fluctuations of the parametric derivative of the transmission and reflection coefficients in absorbing chaotic cavities
Motivated by recent theoretical and experimental works, we study the
statistical fluctuations of the parametric derivative of the transmission T and
reflection R coefficients in ballistic chaotic cavities in the presence of
absorption. Analytical results for the variance of the parametric derivative of
T and R, with and without time-reversal symmetry, are obtained for both
asymmetric and left-right symmetric cavities. These results are valid for
arbitrary number of channels, in completely agreement with the one channel case
in the absence of absorption studied in the literature.Comment: Modified version as accepted in PR
Statistical wave scattering through classically chaotic cavities in the presence of surface absorption
We propose a model to describe the statistical properties of wave scattering
through a classically chaotic cavity in the presence of surface absorption.
Experimentally, surface absorption could be realized by attaching an "absorbing
patch" to the inner wall of the cavity. In our model, the cavity is connected
to the outside by a waveguide with N open modes (or channels), while an
experimental patch is simulated by an "absorbing mirror" attached to the inside
wall of the cavity; the mirror, consisting of a waveguide that supports Na
channels, with absorption inside and a perfectly reflecting wall at its end, is
described by a subunitary scattering matrix Sa. The number of channels Na, as a
measure of the geometric cross section of the mirror, and the lack of unitarity
of Sa as a measure of absorption, are under our control: these parameters have
an important physical significance for real experiments. The absorption
strength in the cavity is quantified by the trace of the lack of unitarity. The
statistical distribution of the resulting S matrix for N=1 open channel and
only one absorbing channel, Na =1, is solved analytically for the orthogonal
and unitary universality classes, and the results are compared with those
arising from numerical simulations. The relation with other models existing in
the literature, in some of which absorption has a volumetric character, is also
studied.Comment: 6 pages, 3 figures, submitted to Phys. Rev.
Intensity correlations in electronic wave propagation in a disordered medium: the influence of spin-orbit scattering
We obtain explicit expressions for the correlation functions of transmission
and reflection coefficients of coherent electronic waves propagating through a
disordered quasi-one-dimensional medium with purely elastic diffusive
scattering in the presence of spin-orbit interactions. We find in the metallic
regime both large local intensity fluctuations and long-range correlations
which ultimately lead to universal conductance fluctuations. We show that the
main effect of spin-orbit scattering is to suppress both local and long-range
intensity fluctuations by a universal symmetry factor 4. We use a scattering
approach based on random transfer matrices.Comment: 15 pages, written in plain TeX, Preprint OUTP-93-42S (University of
Oxford), to appear in Phys. Rev.
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