192 research outputs found
Algebraic structure of stochastic expansions and efficient simulation
We investigate the algebraic structure underlying the stochastic Taylor
solution expansion for stochastic differential systems.Our motivation is to
construct efficient integrators. These are approximations that generate strong
numerical integration schemes that are more accurate than the corresponding
stochastic Taylor approximation, independent of the governing vector fields and
to all orders. The sinhlog integrator introduced by Malham & Wiese (2009) is
one example. Herein we: show that the natural context to study stochastic
integrators and their properties is the convolution shuffle algebra of
endomorphisms; establish a new whole class of efficient integrators; and then
prove that, within this class, the sinhlog integrator generates the optimal
efficient stochastic integrator at all orders.Comment: 19 page
Emerging materials for spin-charge interconversion
International audienc
Shuffle relations for regularised integrals of symbols
We prove shuffle relations which relate a product of regularised integrals of
classical symbols to regularised nested (Chen) iterated integrals, which hold
if all the symbols involved have non-vanishing residue. This is true in
particular for non-integer order symbols. In general the shuffle relations hold
up to finite parts of corrective terms arising from renormalisation on tensor
products of classical symbols, a procedure adapted from renormalisation
procedures on Feynman diagrams familiar to physicists. We relate the shuffle
relations for regularised integrals of symbols with shuffle relations for
multizeta functions adapting the above constructions to the case of symbols on
the unit circle.Comment: 40 pages,latex. Changes concern sections 4 and 5 : an error in
section 4 has been corrected, and the link between section 5 and the previous
ones has been precise
Description of current-driven torques in magnetic tunnel junctions
A free electron description of spin-dependent tranport in magnetic tunnel
junctions with non collinear magnetizations is presented. We investigate the
origin of transverse spin density in tunnelling transport and the quantum
interferences which give rise to oscillatory torques on the local
magnetization. Spin transfer torque is also analyzed and an important bias
asymmetry is found as well as a damped oscillatory behaviour. Furthermore, we
investigate the influence of the s-d exchange coupling on torque in particular
in the case of half-metallic MTJ in which the spin transfer torque is due to
interfacial spin-dependent reflections
A Perspective on Regularization and Curvature
A global connection on the Connes Marcolli renormalization bundle relates
-functions of a class of regularization schemes by gauge
transformations, as well as local solutions to -functions over curved
space-time.Comment: As publishe
Experimental observation of the optical spin-orbit torque
Spin polarized carriers electrically injected into a magnet from an external
polarizer can exert a spin transfer torque (STT) on the magnetization. The phe-
nomenon belongs to the area of spintronics research focusing on manipulating
magnetic moments by electric fields and is the basis of the emerging
technologies for scalable magnetoresistive random access memories. In our
previous work we have reported experimental observation of the optical
counterpart of STT in which a circularly polarized pump laser pulse acts as the
external polarizer, allowing to study and utilize the phenomenon on several
orders of magnitude shorter timescales than in the electric current induced
STT. Recently it has been theoretically proposed and experimentally
demonstrated that in the absence of an external polarizer, carriers in a magnet
under applied electric field can develop a non-equilibrium spin polarization
due to the relativistic spin-orbit coupling, resulting in a current induced
spin-orbit torque (SOT) acting on the magnetization. In this paper we report
the observation of the optical counterpart of SOT. At picosecond time-scales,
we detect excitations of magnetization of a ferromagnetic semiconductor
(Ga,Mn)As which are independent of the polarization of the pump laser pulses
and are induced by non-equilibrium spin-orbit coupled photo-holes.Comment: 4 figure, supplementary information. arXiv admin note: text overlap
with arXiv:1101.104
Backward error analysis and the substitution law for Lie group integrators
Butcher series are combinatorial devices used in the study of numerical
methods for differential equations evolving on vector spaces. More precisely,
they are formal series developments of differential operators indexed over
rooted trees, and can be used to represent a large class of numerical methods.
The theory of backward error analysis for differential equations has a
particularly nice description when applied to methods represented by Butcher
series. For the study of differential equations evolving on more general
manifolds, a generalization of Butcher series has been introduced, called
Lie--Butcher series. This paper presents the theory of backward error analysis
for methods based on Lie--Butcher series.Comment: Minor corrections and additions. Final versio
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