413 research outputs found
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
Enhanced Shot Noise in Tunneling through a Stack of Coupled Quantum Dots
We have investigated the noise properties of the tunneling current through
vertically coupled self-assembled InAs quantum dots. We observe
super-Poissonian shot noise at low temperatures. For increased temperature this
effect is suppressed. The super-Poissonian noise is explained by capacitive
coupling between different stacks of quantum dots
Shot noise in the chaotic-to-regular crossover regime
We investigate the shot noise for phase-coherent quantum transport in the
chaotic-to-regular crossover regime. Employing the Modular Recursive Green's
Function Method for both ballistic and disordered two-dimensional cavities we
find the Fano factor and the transmission eigenvalue distribution for regular
systems to be surprisingly similar to those for chaotic systems. We argue that
in the case of regular dynamics in the cavity, diffraction at the lead openings
is the dominant source of shot noise. We also explore the onset of the
crossover from quantum to classical transport and develop a quasi-classical
transport model for shot noise suppression which agrees with the numerical
quantum data.Comment: 4 pages, 3 figures, submitted to Phys.Rev.Let
Phase transitions in soft-committee machines
Equilibrium statistical physics is applied to layered neural networks with
differentiable activation functions. A first analysis of off-line learning in
soft-committee machines with a finite number (K) of hidden units learning a
perfectly matching rule is performed. Our results are exact in the limit of
high training temperatures. For K=2 we find a second order phase transition
from unspecialized to specialized student configurations at a critical size P
of the training set, whereas for K > 2 the transition is first order. Monte
Carlo simulations indicate that our results are also valid for moderately low
temperatures qualitatively. The limit K to infinity can be performed
analytically, the transition occurs after presenting on the order of N K
examples. However, an unspecialized metastable state persists up to P= O (N
K^2).Comment: 8 pages, 4 figure
Shot Noise and Full Counting Statistics from Non-equilibrium Plasmons in Luttinger-Liquid Junctions
We consider a quantum wire double junction system with each wire segment
described by a spinless Luttinger model, and study theoretically shot noise in
this system in the sequential tunneling regime. We find that the
non-equilibrium plasmonic excitations in the central wire segment give rise to
qualitatively different behavior compared to the case with equilibrium
plasmons. In particular, shot noise is greatly enhanced by them, and exceeds
the Poisson limit. We show that the enhancement can be explained by the
emergence of several current-carrying processes, and that the effect disappears
if the channels effectively collapse to one due to, {\em e.g.}, fast plasmon
relaxation processes.Comment: 9 pages; IOP Journal style; several changes in the tex
Quantum suppression of shot noise in field emitters
We have analyzed the shot noise of electron emission under strong applied
electric fields within the Landauer-Buttiker scheme. In contrast to the
previous studies of vacuum-tube emitters, we show that in new generation
electron emitters, scaled down to the nanometer dimensions, shot noise much
smaller than the Schottky noise is observable. Carbon nanotube field emitters
are among possible candidates to observe the effect of shot-noise suppression
caused by quantum partitioning.Comment: 5 pages, 1 fig, minor changes, published versio
Simple good approximations for the special elliptic functions in standard Fowler-Nordheim tunneling theory for a Schottky-Nordheim barrier
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
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
Electronic thermal transport in strongly correlated multilayered nanostructures
The formalism for a linear-response many-body treatment of the electronic
contributions to thermal transport is developed for multilayered
nanostructures. By properly determining the local heat-current operator, it is
possible to show that the Jonson-Mahan theorem for the bulk can be extended to
inhomogeneous problems, so the various thermal-transport coefficient integrands
are related by powers of frequency (including all effects of vertex corrections
when appropriate). We illustrate how to use this formalism by showing how it
applies to measurements of the Peltier effect, the Seebeck effect, and the
thermal conductance.Comment: 17 pages, 4 figures, submitted to Phys. Rev.
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