644 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
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
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
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
Lattice dynamics of mixed semiconductors (Be,Zn)Se from first-principles calculations
Vibration properties of Zn(1-x)Be(x)Se, a mixed II-VI semiconductor
haracterized by a high contrast in elastic properties of its pure constituents,
ZnSe and BeSe, are simulated by first-principles calculations of electronic
structure, lattice relaxation and frozen phonons. The calculations within the
local density approximation has been done with the Siesta method, using
norm-conserving pseudopotentials and localized basis functions; the benchmark
calculations for pure endsystems were moreover done also by all-electron WIEN2k
code. An immediate motivation for the study was to analyze, at the microscopic
level, the appearance of anomalous phonon modes early detected in Raman spectra
in the intermediate region (20 to 80%) of ZnBe concentration. This was early
discussed on the basis of a percolation phenomenon, i.e., the result of the
formation of wall-to-wall --Be--Se-- chains throughout the crystal. The
presence of such chains was explicitly allowed in our simulation and indeed
brought about a softening and splitting off of particular modes, in accordance
with experimental observation, due to a relative elongation of Be--Se bonds
along the chain as compared to those involving isolated Be atoms. The variation
of force constants with interatomic distances shows common trends in relative
independence on the short-range order.Comment: 11 pages, 10 figures, to be published in Phys. Rev.
Evidence of anisotropic magnetic polarons in laSrMnO by neutron scattering and comparison with Ca-doped manganites
Elastic and inelastic neutron scattering experiments have been performed in a
LaSrMnO untwinned crystal, which exhibits an
antiferromagnetic canted magnetic structure with ferromagnetic layers.
The elastic small q scattering exhibits a modulation with an anisotropic
q-dependence. It can be pictured by ferromagnetic inhomogeneities or polarons
with a platelike shape, the largest size () and largest
inter-polaron distance ( 38) being within the ferromagnetic
layers. Comparison with observations performed on Ca-doped samples, which show
the growth of the magnetic polarons with doping, suggests that this growth is
faster for the Sr than for the Ca substitution. Below the gap of the spin wave
branch typical of the AF layered magnetic structure, an additional spin wave
branch reveals a ferromagnetic and isotropic coupling, already found in
Ca-doped samples. Its q-dependent intensity, very anisotropic, closely reflects
the ferromagnetic correlations found for the static clusters. All these results
agree with a two-phase electronic segregation occurring on a very small scale,
although some characteristics of a canted state are also observed suggesting a
weakly inhomogeneous state.Comment: 11 pages, 11 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
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
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