8,838 research outputs found
Scattering Theory of Current-Induced Spin Polarization
We construct a novel scattering theory to investigate magnetoelectrically
induced spin polarizations. Local spin polarizations generated by electric
currents passing through a spin-orbit coupled mesoscopic system are measured by
an external probe. The electrochemical and spin-dependent chemical potentials
on the probe are controllable and tuned to values ensuring that neither charge
nor spin current flow between the system and the probe, on time-average. For
the relevant case of a single-channel probe, we find that the resulting
potentials are exactly independent of the transparency of the contact between
the probe and the system. Assuming that spin relaxation processes are absent in
the probe, we therefore identify the local spin-dependent potentials in the
sample at the probe position, and hence the local current-induced spin
polarization, with the spin-dependent potentials in the probe itself. The
statistics of these local chemical potentials is calculated within random
matrix theory. While they vanish on spatial and mesoscopic average, they
exhibit large fluctuations, and we show that single systems typically have spin
polarizations exceeding all known current-induced spin polarizations by a
parametrically large factor. Our theory allows to calculate quantum
correlations between spin polarizations inside the sample and spin currents
flowing out of it. We show that these large polarizations correlate only weakly
with spin currents in external leads, and that only a fraction of them can be
converted into a spin current in the linear regime of transport, which is
consistent with the mesoscopic universality of spin conductance fluctuations.
We numerically confirm the theory.Comment: Final version; a tunnel barrier between the probe and the dot is
considered. To appear in 'Nanotechnology' in the special issue on "Quantum
Science and Technology at the Nanoscale
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
Weak and Electromagnetic Nuclear Decay Signatures for Neutrino Reactions in SuperKamiokande
We suggest the study of events in the SuperKamiokande neutrino data due to
charged- and neutral-current neutrino reactions followed by weak and/or
electromagnetic decays of struck nuclei and fragments thereof. This study could
improve the prospects of obtaining evidence for production from oscillations and could augment the data sample used to disfavor
oscillations.Comment: 7 pages, latex, to appear in Phys. Rev. Let
Analysis of ensemble learning using simple perceptrons based on online learning theory
Ensemble learning of nonlinear perceptrons, which determine their outputs
by sign functions, is discussed within the framework of online learning and
statistical mechanics. One purpose of statistical learning theory is to
theoretically obtain the generalization error. This paper shows that ensemble
generalization error can be calculated by using two order parameters, that is,
the similarity between a teacher and a student, and the similarity among
students. The differential equations that describe the dynamical behaviors of
these order parameters are derived in the case of general learning rules. The
concrete forms of these differential equations are derived analytically in the
cases of three well-known rules: Hebbian learning, perceptron learning and
AdaTron learning. Ensemble generalization errors of these three rules are
calculated by using the results determined by solving their differential
equations. As a result, these three rules show different characteristics in
their affinity for ensemble learning, that is ``maintaining variety among
students." Results show that AdaTron learning is superior to the other two
rules with respect to that affinity.Comment: 30 pages, 17 figure
Edge spin accumulation in a ballistic regime
We consider a mesoscopic {\it ballistic} structure with Rashba spin-orbit
splitting of the electron spectrum. The ballistic region is attached to the
leads with a voltage applied between them. We calculate the edge spin density
which appears in the presence of a charge current through the structure due to
the difference in populations of electrons coming from different leads.
Combined effect of the boundary scattering and spin precession leads to
oscillations of the edge polarization with the envelope function decaying as a
power law of the distance from the boundary. The problem is solved with the use
of scattering states. The simplicity of the method allows to gain an insight
into the underlaying physics. We clarify the role of the unitarity of
scattering for the problem of edge spin accumulation. In case of a straight
boundary it leads to exact cancellation of all long-wave oscillations of the
spin density. As a result, only the Friedel-like spin density oscillations with
the momentum 2k_F survive. However, this appears to be rather exceptional case.
In general, the smooth spin oscillations with the spin precession length
recover, as it happens, e.g., for the wiggly boundary. We demonstrate also,
that there is no relation between the spin current in the bulk, which is zero
in the considered case, and the edge spin accumulation.Comment: Latex, 6 pages, 2 fig
- …