3,208 research outputs found
Loop Groups and Discrete KdV Equations
A study is presented of fully discretized lattice equations associated with
the KdV hierarchy. Loop group methods give a systematic way of constructing
discretizations of the equations in the hierarchy. The lattice KdV system of
Nijhoff et al. arises from the lowest order discretization of the trivial,
lowest order equation in the hierarchy, b_t=b_x. Two new discretizations are
also given, the lowest order discretization of the first nontrivial equation in
the hierarchy, and a "second order" discretization of b_t=b_x. The former,
which is given the name "full lattice KdV" has the (potential) KdV equation as
a standard continuum limit. For each discretization a Backlund transformation
is given and soliton content analyzed. The full lattice KdV system has, like
KdV itself, solitons of all speeds, whereas both other discretizations studied
have a limited range of speeds, being discretizations of an equation with
solutions only of a fixed speed.Comment: LaTeX, 23 pages, 1 figur
On the Angular Dependence of the Radiative Gluon Spectrum
The induced momentum spectrum of soft gluons radiated from a high energy
quark produced in and propagating through a QCD medium is reexamined in the
BDMPS formalism. A mistake in our published work (Physical Review C60 (1999)
064902) is corrected. The correct dependence of the fractional induced loss
as a universal function of the variable
where is the size of the medium and
the transport coefficient is presented. We add the proof that the
radiated gluon momentum spectrum derived in our formalism is equivalent with
the one derived in the Zakharov-Wiedemann approach.Comment: LaTex, 5 pages, 1 figur
Control of cellular automata
We study the problem of master-slave synchronization and control of
totalistic cellular automata (CA) by putting a fraction of sites of the slave
equal to those of the master and finding the distance between both as a
function of this fraction. We present three control strategies that exploit
local information about the CA, mainly, the number of nonzero Boolean
derivatives. When no local information is used, we speak of synchronization. We
find the critical properties of control and discuss the best control strategy
compared with synchronization
Multilinear Operators: The Natural Extension Of Hirota's Bilinear Formalism
We introduce multilinear operators, that generalize Hirota's bilinear
operator, based on the principle of gauge invariance of the functions.
We show that these operators can be constructed systematically using the
bilinear 's as building blocks. We concentrate in particular on the
trilinear case and study the possible integrability of equations with one
dependent variable. The 5th order equation of the Lax-hierarchy as well as
Satsuma's lowest-order gauge invariant equation are shown to have simple
trilinear expressions. The formalism can be extended to an arbitrary degree of
multilinearity.Comment: 9 pages in plain Te
Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
Starting from a microscopic tight-binding model and using second order
perturbation theory, we derive explicit expressions for the intrinsic and
Rashba spin-orbit interaction induced gaps in the Dirac-like low-energy band
structure of an isolated graphene sheet. The Rashba interaction parameter is
first order in the atomic carbon spin-orbit coupling strength and first
order in the external electric field perpendicular to the graphene plane,
whereas the intrinsic spin-orbit interaction which survives at E=0 is second
order in . The spin-orbit terms in the low-energy effective Hamiltonian
have the form proposed recently by Kane and Mele. \textit{Ab initio} electronic
structure calculations were performed as a partial check on the validity of the
tight-binding model.Comment: 5 pages, 2 figures; typos corrected, references update
Nuclear Magnetic Quadrupole Moments in Single Particle Approximation
A static magnetic quadrupole moment of a nucleus, induced by T- and P-odd
nucleon-nucleon interaction, is investigated in the single-particle
approximation. Models are considered allowing for analytical solution. The
problem is also treated numerically in a Woods-Saxon potential with spin-orbit
interaction. The stability of results is discussed.Comment: LATEX, 9 pages, 1 postscript figure available upon request from
"[email protected]". BINP 94-4
Neural Network Model for Apparent Deterministic Chaos in Spontaneously Bursting Hippocampal Slices
A neural network model that exhibits stochastic population bursting is
studied by simulation. First return maps of inter-burst intervals exhibit
recurrent unstable periodic orbit (UPO)-like trajectories similar to those
found in experiments on hippocampal slices. Applications of various control
methods and surrogate analysis for UPO-detection also yield results similar to
those of experiments. Our results question the interpretation of the
experimental data as evidence for deterministic chaos and suggest caution in
the use of UPO-based methods for detecting determinism in time-series data.Comment: 4 pages, 5 .eps figures (included), requires psfrag.sty (included
Noise resistance of adiabatic quantum computation using random matrix theory
Besides the traditional circuit-based model of quantum computation, several
quantum algorithms based on a continuous-time Hamiltonian evolution have
recently been introduced, including for instance continuous-time quantum walk
algorithms as well as adiabatic quantum algorithms. Unfortunately, very little
is known today on the behavior of these Hamiltonian algorithms in the presence
of noise. Here, we perform a fully analytical study of the resistance to noise
of these algorithms using perturbation theory combined with a theoretical noise
model based on random matrices drawn from the Gaussian Orthogonal Ensemble,
whose elements vary in time and form a stationary random process.Comment: 9 pages, 3 figure
Dressing chain for the acoustic spectral problem
The iterations are studied of the Darboux transformation for the generalized
Schroedinger operator. The applications to the Dym and Camassa-Holm equations
are considered.Comment: 16 pages, 6 eps figure
- …