676 research outputs found
Derivation of the Zakharov equations
This paper continues the study of the validity of the Zakharov model
describing Langmuir turbulence. We give an existence theorem for a class of
singular quasilinear equations. This theorem is valid for well-prepared initial
data. We apply this result to the Euler-Maxwell equations describing
laser-plasma interactions, to obtain, in a high-frequency limit, an asymptotic
estimate that describes solutions of the Euler-Maxwell equations in terms of
WKB approximate solutions which leading terms are solutions of the Zakharov
equations. Because of transparency properties of the Euler-Maxwell equations,
this study is led in a supercritical (highly nonlinear) regime. In such a
regime, resonances between plasma waves, electromagnetric waves and acoustic
waves could create instabilities in small time. The key of this work is the
control of these resonances. The proof involves the techniques of geometric
optics of Joly, M\'etivier and Rauch, recent results of Lannes on norms of
pseudodifferential operators, and a semiclassical, paradifferential calculus
Characterization of the nanophase precipitation in a metastable beta titanium-based alloy by electrical resistivity, dilatometry and neutron diffraction
The metastable beta Ti-6Mo-5Ta-4Fe (wt.%) alloys was synthesized by cold crucible levitation melting and then quenched in water from the beta phase field. In order to investigate the transformation sequence upon heating, thermal analysis methods such as electrical resistivity, dilatometry and neutron thermodiffraction were employed. By these methods, the different temperatures of transition were detected and solute partitioning was oberved to the beta matrix during the omega and alpha nanophase precipitatio
Lyapunov exponents, one-dimensional Anderson localisation and products of random matrices
The concept of Lyapunov exponent has long occupied a central place in the
theory of Anderson localisation; its interest in this particular context is
that it provides a reasonable measure of the localisation length. The Lyapunov
exponent also features prominently in the theory of products of random matrices
pioneered by Furstenberg. After a brief historical survey, we describe some
recent work that exploits the close connections between these topics. We review
the known solvable cases of disordered quantum mechanics involving random point
scatterers and discuss a new solvable case. Finally, we point out some
limitations of the Lyapunov exponent as a means of studying localisation
properties.Comment: LaTeX, 23 pages, 3 pdf figures ; review for a special issue on
"Lyapunov analysis" ; v2 : typo corrected in eq.(3) & minor change
Functionals of the Brownian motion, localization and metric graphs
We review several results related to the problem of a quantum particle in a
random environment.
In an introductory part, we recall how several functionals of the Brownian
motion arise in the study of electronic transport in weakly disordered metals
(weak localization).
Two aspects of the physics of the one-dimensional strong localization are
reviewed : some properties of the scattering by a random potential (time delay
distribution) and a study of the spectrum of a random potential on a bounded
domain (the extreme value statistics of the eigenvalues).
Then we mention several results concerning the diffusion on graphs, and more
generally the spectral properties of the Schr\"odinger operator on graphs. The
interest of spectral determinants as generating functions characterizing the
diffusion on graphs is illustrated.
Finally, we consider a two-dimensional model of a charged particle coupled to
the random magnetic field due to magnetic vortices. We recall the connection
between spectral properties of this model and winding functionals of the planar
Brownian motion.Comment: Review article. 50 pages, 21 eps figures. Version 2: section 5.5 and
conclusion added. Several references adde
The Local Time Distribution of a Particle Diffusing on a Graph
We study the local time distribution of a Brownian particle diffusing along
the links on a graph. In particular, we derive an analytic expression of its
Laplace transform in terms of the Green's function on the graph. We show that
the asymptotic behavior of this distribution has non-Gaussian tails
characterized by a nontrivial large deviation function.Comment: 8 pages, two figures (included
Bound states in the continuum in open Aharonov-Bohm rings
Using formalism of effective Hamiltonian we consider bound states in
continuum (BIC). They are those eigen states of non-hermitian effective
Hamiltonian which have real eigen values. It is shown that BICs are orthogonal
to open channels of the leads, i.e. disconnected from the continuum. As a
result BICs can be superposed to transport solution with arbitrary coefficient
and exist in propagation band. The one-dimensional Aharonov-Bohm rings that are
opened by attaching single-channel leads to them allow exact consideration of
BICs. BICs occur at discrete values of energy and magnetic flux however it's
realization strongly depend on a way to the BIC's point.Comment: 5 pgaes, 4 figure
Mn local moments prevent superconductivity in iron-pnictides Ba(Fe 1-x Mn x)2As2
75As nuclear magnetic resonance (NMR) experiments were performed on
Ba(Fe1-xMnx)2As2 (xMn = 2.5%, 5% and 12%) single crystals. The Fe layer
magnetic susceptibility far from Mn atoms is probed by the75As NMR line shift
and is found similar to that of BaFe2As2, implying that Mn does not induce
charge doping. A satellite line associated with the Mn nearest neighbours
(n.n.) of 75As displays a Curie-Weiss shift which demonstrates that Mn carries
a local magnetic moment. This is confirmed by the main line broadening typical
of a RKKY-like Mn-induced staggered spin polarization. The Mn moment is due to
the localization of the additional Mn hole. These findings explain why Mn does
not induce superconductivity in the pnictides contrary to other dopants such as
Co, Ni, Ru or K.Comment: 6 pages, 7 figure
Nature of the bad metallic behavior of Fe_{1.06}Te inferred from its evolution in the magnetic state
We investigate with angle resolved photoelectron spectroscopy the change of
the Fermi Surface (FS) and the main bands from the paramagnetic (PM) state to
the antiferromagnetic (AFM) occurring below 72 K in Fe_{1.06}Te. The evolution
is completely different from that observed in iron-pnictides as nesting is
absent. The AFM state is a rather good metal, in agreement with our magnetic
band structure calculation. On the other hand, the PM state is very anomalous
with a large pseudogap on the electron pocket that closes in the AFM state. We
discuss this behavior in connection with spin fluctuations existing above the
magnetic transition and the correlations predicted in the spin-freezing regime
of the incoherent metallic state
Statistics of resonances and of delay times in quasiperiodic Schr"odinger equations
We study the statistical distributions of the resonance widths , and of delay times in one dimensional
quasi-periodic tight-binding systems with one open channel. Both quantities are
found to decay algebraically as , and on
small and large scales respectively. The exponents , and are
related to the fractal dimension of the spectrum of the closed system
as and . Our results are verified for the
Harper model at the metal-insulator transition and for Fibonacci lattices.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let
Resonances for "large" ergodic systems in one dimension: a review
The present note reviews recent results on resonances for one-dimensional
quantum ergodic systems constrained to a large box. We restrict ourselves to
one dimensional models in the discrete case. We consider two type of ergodic
potentials on the half-axis, periodic potentials and random potentials. For
both models, we describe the behavior of the resonances near the real axis for
a large typical sample of the potential. In both cases, the linear density of
their real parts is given by the density of states of the full ergodic system.
While in the periodic case, the resonances distribute on a nice analytic curve
(once their imaginary parts are suitably renormalized), In the random case, the
resonances (again after suitable renormalization of both the real and imaginary
parts) form a two dimensional Poisson cloud
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