287 research outputs found
On quantization of quadratic Poisson structures
Any classical r-matrix on the Lie algebra of linear operators on a real
vector space V gives rise to a quadratic Poisson structure on V which admits a
deformation quantization stemming from the construction of V. Drinfel'd. We
exhibit in this article an example of quadratic Poisson structure which does
not arise this way.Comment: Submitted to Comm. Math. Phys. Version 2 : error in introduction
correcte
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
Signatures of asymmetric and inelastic tunneling on the spin torque bias dependence
The influence of structural asymmetries (barrier height and exchange
splitting), as well as inelastic scattering (magnons and phonons) on the bias
dependence of the spin transfer torque in a magnetic tunnel junction is studied
theoretically using the free electron model. We show that they modify the
"conventional" bias dependence of the spin transfer torque, together with the
bias dependence of the conductance. In particular, both structural asymmetries
and bulk (inelastic) scattering add {\em antisymmetric} terms to the
perpendicular torque ( and ), while the interfacial
inelastic scattering conserves the junction symmetry and only produces {\em
symmetric} terms (, ). The analysis of spin
torque and conductance measurements displays a signature revealing the origin
(asymmetry or inelastic scattering) of the discrepancy
Geometrically relating momentum cut-off and dimensional regularization
The function for a scalar field theory describes the dependence of
the coupling constant on the renormalization mass scale. This dependence is
affected by the choice of regularization scheme. I explicitly relate the
-functions of momentum cut-off regularization and dimensional
regularization on scalar field theories by a gauge transformation using the
Hopf algebras of the Feynman diagrams of the theories.Comment: As submitted to IJGMMP; International Journal of Geometric Methods in
Mathematical Physics, 2013, Volume 10, Number
Crossover from Diffusive to Superfluid Transport in Frustrated Magnets
We investigate the spin transport across the magnetic phase diagram of a
frustrated antiferromagnetic insulator and uncover a drastic modification of
the transport regime from spin diffusion to spin superfluidity. Adopting a
triangular lattice accounting for both nearest neighbor and next-nearest
neighbor exchange interactions with easy-plane anisotropy, we perform atomistic
spin simulations on a two-terminal configuration across the full magnetic phase
diagram. We found that as long as the ground state magnetic moments remain
in-plane, irrespective of whether the magnetic configuration is ferromagnetic,
collinear or non-collinear antiferromagnetic, the system exhibits spin
superfluid behavior with a device output that is independent on the value of
the exchange interactions. When the magnetic frustration is large enough to
compete with the easy-plane anisotropy and cant the magnetic moments out of the
plane, the spin transport progressively evolves towards the diffusive regime.
The robustness of spin superfluidity close to magnetic phase boundaries is
investigated and we uncover the possibility for {\em proximate} spin
superfluidity close to the ferromagnetic transition.Comment: 9 pages, 7 figure
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
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