277 research outputs found
On the mean density of complex eigenvalues for an ensemble of random matrices with prescribed singular values
Given any fixed positive semi-definite diagonal matrix
we derive the explicit formula for the density of complex eigenvalues for
random matrices of the form } where the random unitary
matrices are distributed on the group according to the Haar
measure.Comment: 10 pages, 1 figur
Electrically Driven Light Emission from Individual CdSe Nanowires
We report electroluminescence (EL) measurements carried out on three-terminal
devices incorporating individual n-type CdSe nanowires. Simultaneous optical
and electrical measurements reveal that EL occurs near the contact between the
nanowire and a positively biased electrode or drain. The surface potential
profile, obtained by using Kelvin probe microscopy, shows an abrupt potential
drop near the position of the EL spot, while the band profile obtained from
scanning photocurrent microscopy indicates the existence of an n-type Schottky
barrier at the interface. These observations indicate that light emission
occurs through a hole leakage or an inelastic scattering induced by the rapid
potential drop at the nanowire-electrode interface.Comment: 12 pages, 4 figure
Delocalization of slowly damped eigenmodes on Anosov manifolds
We look at the properties of high frequency eigenmodes for the damped wave
equation on a compact manifold with an Anosov geodesic flow. We study
eigenmodes with spectral parameters which are asymptotically close enough to
the real axis. We prove that such modes cannot be completely localized on
subsets satisfying a condition of negative topological pressure. As an
application, one can deduce the existence of a "strip" of logarithmic size
without eigenvalues below the real axis under this dynamical assumption on the
set of undamped trajectories.Comment: 28 pages; compared with version 1, minor modifications, add two
reference
Complex zeros of real ergodic eigenfunctions
We determine the limit distribution (as ) of complex
zeros for holomorphic continuations \phi_{\lambda}^{\C} to Grauert tubes of
real eigenfunctions of the Laplacian on a real analytic compact Riemannian
manifold with ergodic geodesic flow. If is an
ergodic sequence of eigenfunctions, we prove the weak limit formula
\frac{1}{\lambda_j} [Z_{\phi_{j_k}^{\C}}] \to \frac{i}{\pi} \bar{\partial}
{\partial} |\xi|_g, where [Z_{\phi_{j_k}^{\C}}] is the current of
integration over the complex zeros and where is with respect
to the adapted complex structure of Lempert-Sz\"oke and Guillemin-Stenzel.Comment: Added some examples and references. Also added a new Corollary, and
corrected some typo
Crystal properties of eigenstates for quantum cat maps
Using the Bargmann-Husimi representation of quantum mechanics on a torus
phase space, we study analytically eigenstates of quantized cat maps. The
linearity of these maps implies a close relationship between classically
invariant sublattices on the one hand, and the patterns (or `constellations')
of Husimi zeros of certain quantum eigenstates on the other hand. For these
states, the zero patterns are crystals on the torus. As a consequence, we can
compute explicit families of eigenstates for which the zero patterns become
uniformly distributed on the torus phase space in the limit . This
result constitutes a first rigorous example of semi-classical equidistribution
for Husimi zeros of eigenstates in quantized one-dimensional chaotic systems.Comment: 43 pages, LaTeX, including 7 eps figures Some amendments were made in
order to clarify the text, mainly in the 4 first sections. Figures are
unchanged. To be published in: Nonlinearit
Predicting Global Irradiance Combining Forecasting Models Through Machine Learning
This paper has been presented at : 13th International Conference on Hybrid Artificial Intelligence Systems (HAIS 2018)Predicting solar irradiance is an active research problem, with many physical models having being designed to accurately predict Global Horizontal Irradiance. However, some of the models are better at short time horizons, while others are more accurate for medium and long horizons. The aim of this research is to automatically combine the predictions of four different models (Smart Persistence, Satellite, Cloud Index Advection and Diffusion, and Solar Weather Research and Forecasting) by means of a state-of-the-art machine learning method (Extreme Gradient Boosting). With this purpose, the four models are used as inputs to the machine learning model, so that the output is an improved Global Irradiance forecast. A 2-year dataset of predictions and measures at one radiometric station in Seville has been gathered to validate the method proposed. Three approaches are studied: a general model, a model for each horizon, and models for groups of horizons. Experimental results show that the machine learning combination of predictors is, on average, more accurate than the predictors themselves.The authors are supported by the Spanish Ministry of Economy and Competitiveness, projects ENE2014-56126-C2-1-R and ENE2014-56126-C2-2-R and FEDER funds. Some of the authors are also funded by the Junta de Andalucía (research group TEP-220)
Entropic bounds on semiclassical measures for quantized one-dimensional maps
Quantum ergodicity asserts that almost all infinite sequences of eigenstates
of a quantized ergodic system are equidistributed in the phase space. On the
other hand, there are might exist exceptional sequences which converge to
different (non-Liouville) classical invariant measures. By the remarkable
result of N. Anantharaman and S. Nonnenmacher math-ph/0610019, arXiv:0704.1564
(with H. Koch), for Anosov geodesic flows the metric entropy of any
semiclassical measure must be bounded from below. The result seems to be
optimal for uniformly expanding systems, but not in general case, where it
might become even trivial if the curvature of the Riemannian manifold is
strongly non-uniform. It has been conjectured by the same authors, that in
fact, a stronger bound (valid in general case) should hold.
In the present work we consider such entropic bounds using the model of
quantized one-dimensional maps. For a certain class of non-uniformly expanding
maps we prove Anantharaman-Nonnenmacher conjecture. Furthermore, for these maps
we are able to construct some explicit sequences of eigenstates which saturate
the bound. This demonstrates that the conjectured bound is actually optimal in
that case.Comment: 38 pages, 4 figure
Anatomy of quantum chaotic eigenstates
The eigenfunctions of quantized chaotic systems cannot be described by
explicit formulas, even approximate ones. This survey summarizes (selected)
analytical approaches used to describe these eigenstates, in the semiclassical
limit. The levels of description are macroscopic (one wants to understand the
quantum averages of smooth observables), and microscopic (one wants
informations on maxima of eigenfunctions, "scars" of periodic orbits, structure
of the nodal sets and domains, local correlations), and often focusses on
statistical results. Various models of "random wavefunctions" have been
introduced to understand these statistical properties, with usually good
agreement with the numerical data. We also discuss some specific systems (like
arithmetic ones) which depart from these random models.Comment: Corrected typos, added a few references and updated some result
Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum
A quantum version of transition state theory based on a quantum normal form
(QNF) expansion about a saddle-centre-...-centre equilibrium point is
presented. A general algorithm is provided which allows one to explictly
compute QNF to any desired order. This leads to an efficient procedure to
compute quantum reaction rates and the associated Gamov-Siegert resonances. In
the classical limit the QNF reduces to the classical normal form which leads to
the recently developed phase space realisation of Wigner's transition state
theory. It is shown that the phase space structures that govern the classical
reaction d ynamicsform a skeleton for the quantum scattering and resonance
wavefunctions which can also be computed from the QNF. Several examples are
worked out explicitly to illustrate the efficiency of the procedure presented.Comment: 132 pages, 31 figures, corrected version, Nonlinearity, 21 (2008)
R1-R11
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