928 research outputs found
Correlation functions of impedance and scattering matrix elements in chaotic absorbing cavities
Wave scattering in chaotic systems with a uniform energy loss (absorption) is
considered. Within the random matrix approach we calculate exactly the energy
correlation functions of different matrix elements of impedance or scattering
matrices for systems with preserved or broken time-reversal symmetry. The
obtained results are valid at any number of arbitrary open scattering channels
and arbitrary absorption. Elastic enhancement factors (defined through the
ratio of the corresponding variance in reflection to that in transmission) are
also discussed.Comment: 10 pages, 2 figures (misprints corrected and references updated in
ver.2); to appear in Acta Phys. Pol. A (Proceedings of the 2nd Workshop on
Quantum Chaos and Localization Phenomena, May 19-22, 2005, Warsaw
Role of electron-electron and electron-phonon interaction effect in the optical conductivity of VO2
We have investigated the charge dynamics of VO2 by optical reflectivity
measurements. Optical conductivity clearly shows a metal-insulator transition.
In the metallic phase, a broad Drude-like structure is observed. On the other
hand, in the insulating phase, a broad peak structure around 1.3 eV is
observed. It is found that this broad structure observed in the insulating
phase shows a temperature dependence. We attribute this to the electron-phonon
interaction as in the photoemission spectra.Comment: 6 pages, 8 figures, accepted for publication in Phys. Rev.
Random matrix description of decaying quantum systems
This contribution describes a statistical model for decaying quantum systems
(e.g. photo-dissociation or -ionization). It takes the interference between
direct and indirect decay processes explicitely into account. The resulting
expressions for the partial decay amplitudes and the corresponding cross
sections may be considered a many-channel many-resonance generalization of
Fano's original work on resonance lineshapes [Phys. Rev 124, 1866 (1961)].
A statistical (random matrix) model is then introduced. It allows to describe
chaotic scattering systems with tunable couplings to the decay channels. We
focus on the autocorrelation function of the total (photo) cross section, and
we find that it depends on the same combination of parameters, as the
Fano-parameter distribution. These combinations are statistical variants of the
one-channel Fano parameter. It is thus possible to study Fano interference
(i.e. the interference between direct and indirect decay paths) on the basis of
the autocorrelation function, and thereby in the regime of overlapping
resonances. It allows us, to study the Fano interference in the limit of
strongly overlapping resonances, where we find a persisting effect on the level
of the weak localization correction.Comment: 16 pages, 2 figure
Statistics of S-matrix poles for chaotic systems with broken time reversal invariance: a conjecture
In the framework of a random matrix description of chaotic quantum scattering
the positions of matrix poles are given by complex eigenvalues of an
effective non-Hermitian random-matrix Hamiltonian. We put forward a conjecture
on statistics of for systems with broken time-reversal invariance and
verify that it allows to reproduce statistical characteristics of Wigner time
delays known from independent calculations. We analyze the ensuing two-point
statistical measures as e.g. spectral form factor and the number variance. In
addition we find the density of complex eigenvalues of real asymmetric matrices
generalizing the recent result by Efetov\cite{Efnh}.Comment: 4 page
The density of stationary points in a high-dimensional random energy landscape and the onset of glassy behaviour
We calculate the density of stationary points and minima of a
dimensional Gaussian energy landscape. We use it to show that the point of
zero-temperature replica symmetry breaking in the equilibrium statistical
mechanics of a particle placed in such a landscape in a spherical box of size
corresponds to the onset of exponential in growth of the
cumulative number of stationary points, but not necessarily the minima. For
finite temperatures we construct a simple variational upper bound on the true
free energy of the version of the problem and show that this
approximation is able to recover the position of the whole de-Almeida-Thouless
line.Comment: a revised and shortened version with a few typos corrected and
references added. To appear in JETP Letter
Inference of kinetic Ising model on sparse graphs
Based on dynamical cavity method, we propose an approach to the inference of
kinetic Ising model, which asks to reconstruct couplings and external fields
from given time-dependent output of original system. Our approach gives an
exact result on tree graphs and a good approximation on sparse graphs, it can
be seen as an extension of Belief Propagation inference of static Ising model
to kinetic Ising model. While existing mean field methods to the kinetic Ising
inference e.g., na\" ive mean-field, TAP equation and simply mean-field, use
approximations which calculate magnetizations and correlations at time from
statistics of data at time , dynamical cavity method can use statistics of
data at times earlier than to capture more correlations at different time
steps. Extensive numerical experiments show that our inference method is
superior to existing mean-field approaches on diluted networks.Comment: 9 pages, 3 figures, comments are welcom
Skew-orthogonal Laguerre polynomials for chiral real asymmetric random matrices
We apply the method of skew-orthogonal polynomials (SOP) in the complex plane to asymmetric random matrices with real elements, belonging to two different classes. Explicit integral representations valid for arbitrary weight functions are derived for the SOP and for their Cauchy transforms, given as expectation values of traces and determinants or their inverses, respectively. Our proof uses the fact that the joint probability distribution function for all combinations of real eigenvalues and complex conjugate eigenvalue pairs can be written as a product. Examples for the SOP are given in terms of Laguerre polynomials for the chiral ensemble (also called the non-Hermitian real Wishart-Laguerre ensemble), both without and with the insertion of characteristic polynomials. Such characteristic polynomials play the role of mass terms in applications to complex Dirac spectra in field theory. In addition, for the elliptic real Ginibre ensemble we recover the SOP of Forrester and Nagao in terms of Hermite polynomials
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