274 research outputs found

### Magnetic states in multiply-connected flat nano-elements

Flat magnetic nano-elements are an essential component of current and future
spintronic devices. By shaping an element it is possible to select and
stabilize chosen metastable magnetic states, control its magnetization
dynamics. Here, using a recent significant development in mathematics of
conformal mapping, complex variable based approach to the description of
magnetic states in planar nano-elements is extended to the case when elements
are multiply-connected (that is, contain holes or magnetic anti-dots). We show
that presence of holes implies a certain restriction on the set of magnetic
states of nano-element.Comment: 5 pages, 7 figure

### 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

### 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 $\alpha$, where $\alpha$
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

### Correlation of internal representations in feed-forward neural networks

Feed-forward multilayer neural networks implementing random input-output
mappings develop characteristic correlations between the activity of their
hidden nodes which are important for the understanding of the storage and
generalization performance of the network. It is shown how these correlations
can be calculated from the joint probability distribution of the aligning
fields at the hidden units for arbitrary decoder function between hidden layer
and output. Explicit results are given for the parity-, and-, and
committee-machines with arbitrary number of hidden nodes near saturation.Comment: 6 pages, latex, 1 figur

### Motion of four-dimensional rigid body around a fixed point: an elementary approach. I

The goal of this note is to give the explicit solution of Euler-Frahm
equations for the Manakov four-dimensional case by elementary means. For this,
we use some results from the original papers by Schottky [Sch 1891], Koetter
[Koe 1892], Weber [We 1878], and Caspary [Ca 1893]. We hope that such approach
will be useful for the solution of the problem of $n$-dimensional top.Comment: LaTeX, 9 page

### 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 $g$

### Excess Noise in Biased Superconducting Weak Links

Non-equilibrium excess noise of a short quasi one-dimensional constriction
between two superconductors is considered. A general expression for the
current-current correlation function valid for arbitrary temperatures and bias
voltages is derived. This formalism is applied to a current-carrying quantum
channel with perfect transparency. Contrary to a transparent channel separating
two normal conductors, a weak link between two superconductors exhibits a
finite level of noise. The source of noise is fractional Andreev scattering of
quasiparticles with energies $|E|$ greater than the half-width $\Delta$ of the
superconducting gap. For high bias voltages, $V \gg \Delta /e$, the relation
between the zero-frequency limit of the noise spectrum, $S(0)$, and the excess
current $I_{\text{exc}}$ reads $S(0)=(1/5)|e|I_{\text{exc}}$. As $\Delta
\rightarrow 0$ both the excess noise and the excess current vanish linearly in
$\Delta$, %$\propto \Delta$, their ratio being constant.Comment: 8 pages (Latex), 1 figur

### Correlations between hidden units in multilayer neural networks and replica symmetry breaking

We consider feed-forward neural networks with one hidden layer, tree
architecture and a fixed hidden-to-output Boolean function. Focusing on the
saturation limit of the storage problem the influence of replica symmetry
breaking on the distribution of local fields at the hidden units is
investigated. These field distributions determine the probability for finding a
specific activation pattern of the hidden units as well as the corresponding
correlation coefficients and therefore quantify the division of labor among the
hidden units. We find that although modifying the storage capacity and the
distribution of local fields markedly replica symmetry breaking has only a
minor effect on the correlation coefficients. Detailed numerical results are
provided for the PARITY, COMMITTEE and AND machines with K=3 hidden units and
nonoverlapping receptive fields.Comment: 9 pages, 3 figures, RevTex, accepted for publication in Phys. Rev.

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