16,507 research outputs found
Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit
Let denote the space of all locally finite subsets (configurations)
in . A stochastic dynamics of binary jumps in continuum is a
Markov process on in which pairs of particles simultaneously hop over
. We discuss a non-equilibrium dynamics of binary jumps. We prove
the existence of an evolution of correlation functions on a finite time
interval. We also show that a Vlasov-type mesoscopic scaling for such a
dynamics leads to a generalized Boltzmann non-linear equation for the particle
density
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.
Storage capacity of correlated perceptrons
We consider an ensemble of single-layer perceptrons exposed to random
inputs and investigate the conditions under which the couplings of these
perceptrons can be chosen such that prescribed correlations between the outputs
occur. A general formalism is introduced using a multi-perceptron costfunction
that allows to determine the maximal number of random inputs as a function of
the desired values of the correlations. Replica-symmetric results for and
are compared with properties of two-layer networks of tree-structure and
fixed Boolean function between hidden units and output. The results show which
correlations in the hidden layer of multi-layer neural networks are crucial for
the value of the storage capacity.Comment: 16 pages, Latex2
On the violation of a local form of the Lieb-Oxford bound
In the framework of density-functional theory, several popular density
functionals for exchange and correlation have been constructed to satisfy a
local form of the Lieb-Oxford bound. In its original global expression, the
bound represents a rigorous lower limit for the indirect Coulomb interaction
energy. Here we employ exact-exchange calculations for the G2 test set to show
that the local form of the bound is violated in an extensive range of both the
dimensionless gradient and the average electron density. Hence, the results
demonstrate the severity in the usage of the local form of the bound in
functional development. On the other hand, our results suggest alternative ways
to construct accurate density functionals for the exchange energy.Comment: (Submitted on 27 April 2012
Robust to impurity-scattering spin Hall effect in two-dimensional electron gas
We propose a mechanism of spin Hall effect in two-dimensional electron gas
with spatially random Rashba spin-orbit interaction. The calculations based on
the Kubo formalism and kinetic equation show that in contrast to the constant
spin-orbit coupling, spin Hall conductivity in the random spin-orbit field is
not totally suppressed by the potential impurity scattering. Even if the
regular contribution is removed by the vertex corrections, the terms we
consider, remain. Therefore, the intrinsic spin-Hall effect exists being,
however, non-universal.Comment: 4+ pages, 2 figure
Structure of the vacuum states in the presence of isovector and isoscalar pairing correlations
The long standing problem of proton-neutron pairing and, in particular, the
limitations imposed on the solutions by the available symmetries, is revisited.
We look for solutions with non-vanishing expectation values of the proton, the
neutron and the isoscalar gaps. For an equal number of protons and neutrons we
find two solutions where the absolute values of proton and neutrons gaps are
equal but have the same or opposite sign. The behavior and structure of these
solutions differ for spin saturated (single l-shell) and spin unsaturared
systems (single j-shell). In the former case the BCS results are checked
against an exact calculation.Comment: 19 pages, 5 postscript figure
Side-jumps in the spin-Hall effect: construction of the Boltzmann collision integral
We present a systematic derivation of the side-jump contribution to the
spin-Hall current in systems without band structure spin-orbit interactions,
focusing on the construction of the collision integral for the Boltzmann
equation. Starting from the quantum Liouville equation for the density operator
we derive an equation describing the dynamics of the density matrix in the
first Born approximation and to first order in the driving electric field.
Elastic scattering requires conservation of the total energy, including the
spin-orbit interaction energy with the electric field: this results in a first
correction to the customary collision integral found in the Born approximation.
A second correction is due to the change in the carrier position during
collisions. It stems from the part of the density matrix off-diagonal in wave
vector. The two corrections to the collision integral add up and are
responsible for the total side-jump contribution to the spin-Hall current. The
spin-orbit-induced correction to the velocity operator also contains terms
diagonal and off-diagonal in momentum space, which together involve the total
force acting on the system. This force is explicitly shown to vanish (on the
average) in the steady state: thus the total contribution to the spin-Hall
current due to the additional terms in the velocity operator is zero.Comment: Added references, expanded discussion, revised introductio
Optical injection and terahertz detection of the macroscopic Berry curvature
We propose an experimental scheme to probe the Berry curvature of solids. Our
method is sensitive to arbitrary regions of the Brillouin zone, and employs
only basic optical and terahertz techniques to yield a background free signal.
Using semiconductor quantum wells as a prototypical system, we discuss how to
inject Berry curvature macroscopically, and probe it in a way that provides
information about the underlying microscopic Berry curvature.Comment: 4 pages, accepted in Physical Review Letter
Analysis of OPM potentials for multiplet states of 3d transition metal atoms
We apply the optimized effective potential method (OPM) to the multiplet
energies of the 3d transition metal atoms, where the orbital dependence of
the energy functional with respect to orbital wave function is the
single-configuration HF form. We find that the calculated OPM exchange
potential can be represented by the following two forms. Firstly, the
difference between OPM exchange potentials of the multiplet states can be
approximated by the linear combination of the potentials derived from the
Slater integrals and for the average
energy of the configuration. Secondly, the OPM exchange potential can be
expressed as the linear combination of the OPM exchange potentials of the
single determinants.Comment: 15 pages, 6 figures, to be published in J. Phys.
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