2,289 research outputs found
Fluctuations and Ergodicity of the Form Factor of Quantum Propagators and Random Unitary Matrices
We consider the spectral form factor of random unitary matrices as well as of
Floquet matrices of kicked tops. For a typical matrix the time dependence of
the form factor looks erratic; only after a local time average over a suitably
large time window does a systematic time dependence become manifest. For
matrices drawn from the circular unitary ensemble we prove ergodicity: In the
limits of large matrix dimension and large time window the local time average
has vanishingly small ensemble fluctuations and may be identified with the
ensemble average. By numerically diagonalizing Floquet matrices of kicked tops
with a globally chaotic classical limit we find the same ergodicity. As a
byproduct we find that the traces of random matrices from the circular
ensembles behave very much like independent Gaussian random numbers. Again,
Floquet matrices of chaotic tops share that universal behavior. It becomes
clear that the form factor of chaotic dynamical systems can be fully faithful
to random-matrix theory, not only in its locally time-averaged systematic time
dependence but also in its fluctuations.Comment: 12 pages, RevTEX, 4 figures in eps forma
Nonlinear statistics of quantum transport in chaotic cavities
Copyright © 2008 The American Physical Society.In the framework of the random matrix approach, we apply the theory of Selberg’s integral to problems of quantum transport in chaotic cavities. All the moments of transmission eigenvalues are calculated analytically up to the fourth order. As a result, we derive exact explicit expressions for the skewness and kurtosis of the conductance and transmitted charge as well as for the variance of the shot-noise power in chaotic cavities. The obtained results are generally valid at arbitrary numbers of propagating channels in the two attached leads. In the particular limit of large (and equal) channel numbers, the shot-noise variance attends the universal value 1∕64β that determines a universal Gaussian statistics of shot-noise fluctuations in this case.DFG and BRIEF
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.
Statistics of quantum transport in chaotic cavities with broken time-reversal symmetry
The statistical properties of quantum transport through a chaotic cavity are
encoded in the traces \T={\rm Tr}(tt^\dag)^n, where is the transmission
matrix. Within the Random Matrix Theory approach, these traces are random
variables whose probability distribution depends on the symmetries of the
system. For the case of broken time-reversal symmetry, we present explicit
closed expressions for the average value and for the variance of \T for all
. In particular, this provides the charge cumulants \Q of all orders. We
also compute the moments of the conductance . All the
results obtained are exact, {\it i.e.} they are valid for arbitrary numbers of
open channels.Comment: 5 pages, 4 figures. v2-minor change
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
Statistical properties of random density matrices
Statistical properties of ensembles of random density matrices are
investigated. We compute traces and von Neumann entropies averaged over
ensembles of random density matrices distributed according to the Bures
measure. The eigenvalues of the random density matrices are analyzed: we derive
the eigenvalue distribution for the Bures ensemble which is shown to be broader
then the quarter--circle distribution characteristic of the Hilbert--Schmidt
ensemble. For measures induced by partial tracing over the environment we
compute exactly the two-point eigenvalue correlation function.Comment: 8 revtex pages with one eps file included, ver. 2 - minor misprints
correcte
Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
Assuming the validity of random matrices for describing the statistics of a
closed chaotic quantum system, we study analytically some statistical
properties of the S-matrix characterizing scattering in its open counterpart.
In the first part of the paper we attempt to expose systematically ideas
underlying the so-called stochastic (Heidelberg) approach to chaotic quantum
scattering. Then we concentrate on systems with broken time-reversal invariance
coupled to continua via M open channels. By using the supersymmetry method we
derive:
(i) an explicit expression for the density of S-matrix poles (resonances) in
the complex energy plane
(ii) an explicit expression for the parametric correlation function of
densities of eigenphases of the S-matrix.
We use it to find the distribution of derivatives of these eigenphases with
respect to the energy ("partial delay times" ) as well as with respect to an
arbitrary external parameter.Comment: 51 pages, RevTEX , three figures are available on request. To be
published in the special issue of the Journal of Mathematical Physic
Trace distance from the viewpoint of quantum operation techniques
In the present paper, the trace distance is exposed within the quantum
operations formalism. The definition of the trace distance in terms of a
maximum over all quantum operations is given. It is shown that for any pair of
different states, there are an uncountably infinite number of maximizing
quantum operations. Conversely, for any operation of the described type, there
are an uncountably infinite number of those pairs of states that the maximum is
reached by the operation. A behavior of the trace distance under considered
operations is studied. Relations and distinctions between the trace distance
and the sine distance are discussed.Comment: 26 pages, no figures. The bibliography is extended, explanatory
improvement
Observations of TeV gamma rays from Markarian 501 at large zenith angles
TeV gamma rays from the blazar Markarian 501 have been detected with the
University of Durham Mark 6 atmospheric Cerenkov telescope using the imaging
technique at large zenith angles. Observations were made at zenith angles in
the range 70 - 73 deg during 1997 July and August when Markarian 501 was
undergoing a prolonged and strong flare.Comment: 7 pages, 2 figures, accepted for publication in J. Phys. G.: Nucl.
Part. Phy
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