349 research outputs found
The non-existence of stable Schottky forms
Let be the Satake compactification of the moduli space of
principally polarized abelian -folds and the closure of the image of
the moduli space of genus curves in under the Jacobian
morphism. Then lies in the boundary of for any . We
prove that and do not meet transversely in , but
rather that their intersection contains the th order infinitesimal
neighbourhood of in . We deduce that there is no non-trivial
stable Siegel modular form that vanishes on for every . In particular,
given two inequivalent positive even unimodular quadratic forms and ,
there is a curve whose period matrix distinguishes between the theta series of
and .Comment: Corrected version, using Yamada's correct version of Fay's formula
for the period matrix of a certain degenerating family of curves. To appear
in Compositio Mathematic
Full counting statistics of chiral Luttinger liquids with impurities
We study the statistics of charge transfer through an impurity in a chiral
Luttinger liquid (realized experimentally as a quantum point contact in a
fractional quantum Hall edge state device). Taking advantage of the
integrability we present a procedure for obtaining the cumulant generating
function of the probability distribution to transfer a fixed amount of charge
through the constriction. Using this approach we analyze in detail the
behaviour of the third cumulant C_3 as a function of applied voltage,
temperature and barrier height. We predict that C_3 can be used to measure the
fractional charge at temperatures, which are several orders of magnitude higher
than those needed to extract the fractional charge from the measurement of the
second cumulant. Moreover, we identify the component of C_3, which carries the
information about the fractional charge.Comment: 5 pages, 2 figures (EPS files
Generalizing with perceptrons in case of structured phase- and pattern-spaces
We investigate the influence of different kinds of structure on the learning
behaviour of a perceptron performing a classification task defined by a teacher
rule. The underlying pattern distribution is permitted to have spatial
correlations. The prior distribution for the teacher coupling vectors itself is
assumed to be nonuniform. Thus classification tasks of quite different
difficulty are included. As learning algorithms we discuss Hebbian learning,
Gibbs learning, and Bayesian learning with different priors, using methods from
statistics and the replica formalism. We find that the Hebb rule is quite
sensitive to the structure of the actual learning problem, failing
asymptotically in most cases. Contrarily, the behaviour of the more
sophisticated methods of Gibbs and Bayes learning is influenced by the spatial
correlations only in an intermediate regime of , where
specifies the size of the training set. Concerning the Bayesian case we show,
how enhanced prior knowledge improves the performance.Comment: LaTeX, 32 pages with eps-figs, accepted by J Phys
Full counting statistics of spin transfer through the Kondo dot
We calculate the spin current distribution function for a Kondo dot in two
different regimes. In the exactly solvable Toulouse limit the linear response,
zero temperature statistics of the spin transfer is trinomial, such that all
the odd moments vanish and the even moments follow a binomial distribution. On
the contrary, the corresponding spin-resolved distribution turns out to be
binomial. The combined spin and charge statistics is also determined. In
particular, we find that in the case of a finite magnetic field or an
asymmetric junction the spin and charge measurements become statistically
dependent. Furthermore, we analyzed the spin counting statistics of a generic
Kondo dot at and around the strong-coupling fixed point (the unitary limit).
Comparing these results with the Toulouse limit calculation we determine which
features of the latter are generic and which ones are artifacts of the spin
symmetry breaking.Comment: 9 pages, 3 eps figure
Shot Noise in Linear Macroscopic Resistors
We report on a direct experimental evidence of shot noise in a linear
macroscopic resistor. The origin of the shot noise comes from the fluctuation
of the total number of charge carriers inside the resistor associated with
their diffusive motion under the condition that the dielectric relaxation time
becomes longer than the dynamic transit time. Present results show that neither
potential barriers nor the absence of inelastic scattering are necessary to
observe shot noise in electronic devices.Comment: 10 pages, 5 figure
Using a quantum dot as a high-frequency shot noise detector
We present the experimental realization of a Quantum Dot (QD) operating as a
high-frequency noise detector. Current fluctuations produced in a nearby
Quantum Point Contact (QPC) ionize the QD and induce transport through excited
states. The resulting transient current through the QD represents our detector
signal. We investigate its dependence on the QPC transmission and voltage bias.
We observe and explain a quantum threshold feature and a saturation in the
detector signal. This experimental and theoretical study is relevant in
understanding the backaction of a QPC used as a charge detector.Comment: 4 pages, 4 figures, accepted for publication in Physical Review
Letter
Wave-packet Formalism of Full Counting Statistics
We make use of the first-quantized wave-packet formulation of the full
counting statistics to describe charge transport of noninteracting electrons in
a mesoscopic device. We derive various expressions for the characteristic
function generating the full counting statistics, accounting for both energy
and time dependence in the scattering process and including exchange effects
due to finite overlap of the incoming wave packets. We apply our results to
describe the generic statistical properties of a two-fermion scattering event
and find, among other features, sub-binomial statistics for nonentangled
incoming states (Slater rank 1), while entangled states (Slater rank 2) may
generate super-binomial (and even super-Poissonian) noise, a feature that can
be used as a spin singlet-triplet detector. Another application is concerned
with the constant-voltage case, where we generalize the original result of
Levitov-Lesovik to account for energy-dependent scattering and finite
measurement time, including short time measurements, where Pauli blocking
becomes important.Comment: 20 pages, 5 figures; major update, new figures and explanations
included as well as a discussion about finite temperatures and subleading
logarithmic term
AC conductance and non-symmetrized noise at finite frequency in quantum wires and carbon nanotubes
We calculate the AC conductance and the finite-frequency non-symmetrized
noise in interacting quantum wires and single-wall carbon nanotubes in the
presence of an impurity. We observe a strong asymmetry in the frequency
spectrum of the non-symmetrized excess noise, even in the presence of the
metallic leads. We find that this asymmetry is proportional to the differential
excess AC conductance of the system, defined as the difference between the AC
differential conductances at finite and zero voltage, and thus disappears for a
linear system. In the quantum regime, for temperatures much smaller than the
frequency and the applied voltage, we find that the emission noise is exactly
equal to the impurity partition noise. For the case of a weak impurity we
expand our results for the AC conductance and the noise perturbatively. In
particular, if the impurity is located in the middle of the wire or at one of
the contacts, our calculations show that the noise exhibits oscillations with
respect to frequency, whose period is directly related to the value of the
interaction parameter
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