542 research outputs found
Conductance Fluctuations, Weak Localization, and Shot Noise for a Ballistic Constriction in a Disordered Wire
This is a study of phase-coherent conduction through a ballistic point
contact with disordered leads. The disorder imposes mesoscopic
(sample-to-sample) fluctuations and weak-localization corrections on the
conductance, and also leads to time-dependent fluctuations (shot noise) of the
current. These effects are computed by means of a mapping onto an unconstricted
conductor with a renormalized mean free path. The mapping holds both in the
metallic and in the localized regime, and permits a solution for arbitrary
ratio of mean free path to sample length. In the case of a single-channel
quantum point contact, the mapping is onto a one-dimensional disordered chain,
for which the complete distribution of the conductance is known. The theory is
supported by numerical simulations. ***Submitted to Physical Review B.****Comment: 15 pages, REVTeX-3.0, 9 postscript figures appended as
self-extracting archive, INLO-PUB-940309
What is the role of the model in socio-hydrology? Discussion of “Prediction in a socio-hydrological world”<sup>*</sup>
Quantum-to-classical crossover for Andreev billiards in a magnetic field
We extend the existing quasiclassical theory for the superconducting
proximity effect in a chaotic quantum dot, to include a time-reversal-symmetry
breaking magnetic field. Random-matrix theory (RMT) breaks down once the
Ehrenfest time becomes longer than the mean time between
Andreev reflections. As a consequence, the critical field at which the
excitation gap closes drops below the RMT prediction as is
increased. Our quasiclassical results are supported by comparison with a fully
quantum mechanical simulation of a stroboscopic model (the Andreev kicked
rotator).Comment: 11 pages, 10 figure
Density of States and Energy Gap in Andreev Billiards
We present numerical results for the local density of states in semiclassical
Andreev billiards. We show that the energy gap near the Fermi energy develops
in a chaotic billiard. Using the same method no gap is found in similar square
and circular billiards.Comment: 9 pages, 6 Postscript figure
Tail States below the Thouless Gap in SNS junctions: Classical Fluctuations
We study the tails of the density of states (DOS) in a diffusive
superconductor-normal metal-superconductor (SNS) junction below the Thouless
gap. We show that long-wave fluctuations of the concentration of impurities in
the normal layer lead to the formation of subgap quasiparticle states, and
calculate the associated subgap DOS in all effective dimensionalities. We
compare the resulting tails with those arising from mesoscopic gap
fluctuations, and determine the dimensionless parameters controlling which
contribution dominates the subgap DOS. We observe that the two contributions
are formally related to each other by a dimensional reduction.Comment: 6 pages, 1 figur
A pseudointegrable Andreev billiard
A circular Andreev billiard in a uniform magnetic field is studied. It is
demonstrated that the classical dynamics is pseudointegrable in the same sense
as for rational polygonal billiards. The relation to a specific polygon, the
asymmetric barrier billiard, is discussed. Numerical evidence is presented
indicating that the Poincare map is typically weak mixing on the invariant
sets. This link between these different classes of dynamical systems throws
some light on the proximity effect in chaotic Andreev billiards.Comment: 5 pages, 5 figures, to appear in PR
Commensurability effects in Andreev antidot billiards
An Andreev billiard was realized in an array of niobium filled antidots in a
high-mobility InAs/AlGaSb heterostructure. Below the critical temperature T_C
of the Nb dots we observe a strong reduction of the resistance around B=0 and a
suppression of the commensurability peaks, which are usually found in antidot
lattices. Both effects can be explained in a classical Kubo approach by
considering the trajectories of charge carriers in the semiconductor, when
Andreev reflection at the semiconductor-superconductor interface is included.
For perfect Andreev reflection, we expect a complete suppression of the
commensurability features, even though motion at finite B is chaotic.Comment: 4 pages, 4 figure
Superconductor-proximity effect in chaotic and integrable billiards
We explore the effects of the proximity to a superconductor on the level
density of a billiard for the two extreme cases that the classical motion in
the billiard is chaotic or integrable. In zero magnetic field and for a uniform
phase in the superconductor, a chaotic billiard has an excitation gap equal to
the Thouless energy. In contrast, an integrable (rectangular or circular)
billiard has a reduced density of states near the Fermi level, but no gap. We
present numerical calculations for both cases in support of our analytical
results. For the chaotic case, we calculate how the gap closes as a function of
magnetic field or phase difference.Comment: 4 pages, RevTeX, 2 Encapsulated Postscript figures. To be published
by Physica Scripta in the proceedings of the "17th Nordic Semiconductor
Meeting", held in Trondheim, June 199
Adiabatic quantization of Andreev levels
We identify the time between Andreev reflections as a classical adiabatic
invariant in a ballistic chaotic cavity (Lyapunov exponent ), coupled
to a superconductor by an -mode point contact. Quantization of the
adiabatically invariant torus in phase space gives a discrete set of periods
, which in turn generate a ladder of excited states
. The largest quantized period is the
Ehrenfest time . Projection of the invariant torus
onto the coordinate plane shows that the wave functions inside the cavity are
squeezed to a transverse dimension , much below the width of
the point contact.Comment: 4 pages, 3 figure
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