703 research outputs found
Expanding Semiflows on Branched Surfaces and One-Parameter Semigroups of Operators
We consider expanding semiflows on branched surfaces. The family of transfer
operators associated to the semiflow is a one-parameter semigroup of operators.
The transfer operators may also be viewed as an operator-valued function of
time and so, in the appropriate norm, we may consider the vector-valued Laplace
transform of this function. We obtain a spectral result on these operators and
relate this to the spectrum of the generator of this semigroup. Issues of
strong continuity of the semigroup are avoided. The main result is the
improvement to the machinery associated with studying semiflows as
one-parameter semigroups of operators and the study of the smoothness
properties of semiflows defined on branched manifolds, without encoding as a
suspension semiflow
High-field AFMR in single-crystalline La_{0.95}Sr_{0.05}MnO_3: Experimental evidence for the existence of a canted magnetic structure
High-field antiferromagnetic-resonance (AFMR) spectra were obtained in the
frequency range 60 GHz < \nu < 700 GHz and for magnetic fields up to 8 T in
twin-free single crystals of La_{0.95}Sr_{0.05}MnO_3. At low temperatures two
antiferromagnetic modes were detected, which reveal different excitation
conditions and magnetic field dependencies. No splitting of these modes was
observed for any orientation of the static magnetic field excluding the
phase-separation scenario for this composition. Instead, the full data set
including the anisotropic magnetization can be well described using a
two-sublattice model of a canted antiferromagnetic structure.Comment: 4 pages, 3 figure
Inhomogeneous Magnetism in La-doped CaMnO3. (II) Mesoscopic Phase Separation due to Lattice-coupled FM Interactions
A detailed investigation of mesoscopic magnetic and crystallographic phase
separation in Ca(1-x)La(x)MnO3, 0.00<=x<=0.20, is reported. Neutron powder
diffraction and DC-magnetization techniques have been used to isolate the
different roles played by electrons doped into the eg level as a function of
their concentration x. The presence of multiple low-temperature magnetic and
crystallographic phases within individual polycrystalline samples is argued to
be an intrinsic feature of the system that follows from the shifting balance
between competing FM and AFM interactions as a function of temperature. FM
double-exchange interactions associated with doped eg electrons are favored
over competing AFM interactions at higher temperatures, and couple more
strongly with the lattice via orbital polarization. These FM interactions
thereby play a privileged role, even at low eg electron concentrations, by
virtue of structural modifications induced above the AFM transition
temperatures.Comment: 8 pages, 7 figure
Approach to the metal-insulator transition in La(1-x)CaxMnO3 (0<x<.2): magnetic inhomogeneity and spin wave anomaly
We describe the evolution of the static and dynamic spin correlations of
LaCaMnO, for x=0.1, 0.125 and 0.2, where the system evolves
from the canted magnetic state towards the insulating ferromagnetic state,
approaching the metallic transition (x=0.22).
In the x=0.1 sample, the observation of two spin wave branches typical of two
distinct types of magnetic coupling, and of a modulation in the elastic diffuse
scattering characteristic of ferromagnetic inhomogeneities, confirms the static
and dynamic inhomogeneous features previously observed at x0.1. The
anisotropic q-dependence of the intensity of the low-energy spin wave suggests
a bidimensionnal character for the static inhomogeneities. At x=0.125, which
corresponds to the occurence of a ferromagnetic and insulating state, the two
spin wave branches reduce to a single one, but anisotropic. At this
concentration, an anomaly appears at {\bf q}=(1.25,1.25,0), that could be
related to an underlying periodicity, as arising from (1.5,1.5,0)
superstructures.
At x=0.2, the spin-wave branch is isotropic. In addition to the anomaly
observed at q, extra magnetic excitations are observed at larger q, forming
an optical branch. The two dispersion curves suggest an anti-crossing behavior
at some {\bf q'} value, which could be explained by a folding due to an
underlying perodicity involving four cubic lattice spacings
Convergence to stable laws for multidimensional stochastic recursions: the case of regular matrices
Given a sequence of i.i.d.\ random variables with
generic copy , we consider the random
difference equation (RDE) , and assume
the existence of such that \lim_{n \to \infty}(\E{\norm{M_1 ...
M_n}^\kappa})^{\frac{1}{n}} = 1 . We prove, under suitable assumptions, that
the sequence , appropriately normalized, converges in
law to a multidimensional stable distribution with index . As a
by-product, we show that the unique stationary solution of the RDE is
regularly varying with index , and give a precise description of its
tail measure. This extends the prior work http://arxiv.org/abs/1009.1728v3 .Comment: 15 page
Higher Kac-Moody algebras and moduli spaces of -bundles
We provide a generalization to the higher dimensional case of the construction of the current algebra g((z)), of its Kac-Moody extension and of the classical results relating them to the theory of G-bundles over a curve. For a reductive algebraic group G with Lie algebra g, we define a dg-Lie algebra g_n of n-dimensional currents in g. We show that any symmetric G-invariant polynomial P on g of degree n+1 determines a central extension of g_n by the base field k that we call higher Kac-Moody algebra g_{n,P} associated to P. Further, for a smooth, projective variety X of dimension n>1, we show that g_n acts infinitesimally on the derived moduli space RBun_G(X,x) of G-bundles over X trivialized at the formal neighborhood of a point x of X. Finally, for a representation \phi: G-->GL_r, we construct an associated determinantal line bundle on RBun_G(X,x) and prove that the action of g_n extends to an action of g_{n,P_\phi} on such bundle for P_\phi the (n+1)-st Chern character of \phi
Inhomogeneous magnetism in La-doped CaMnO3. (I) Nanometric-scale spin clusters and long-range spin canting
Neutron measurements on Ca{1-x}La{x}MnO3 (0.00 <= x <= 0.20) reveal the
development of a liquid-like spatial distribution of magnetic droplets of
average size ~10 Angstroms, the concentration of which is proportional to x
(one cluster per ~60 doped electrons). In addition, a long-range ordered
ferromagnetic component is observed for ~0.05 < x < ~0.14. This component is
perpendicularly coupled to the simple G-type antiferromagnetic (G-AFM)
structure of the undoped compound, which is a signature of a G-AFM + FM
spin-canted state. The possible relationship between cluster formation and the
stabilization of a long-range spin-canting for intermediate doping is
discussed.Comment: Submitted to Physical Review
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