15,616 research outputs found
Mode fluctuations as fingerprint of chaotic and non-chaotic systems
The mode-fluctuation distribution is studied for chaotic as well as
for non-chaotic quantum billiards. This statistic is discussed in the broader
framework of the functions being the probability of finding energy
levels in a randomly chosen interval of length , and the distribution of
, where is the number of levels in such an interval, and their
cumulants . It is demonstrated that the cumulants provide a possible
measure for the distinction between chaotic and non-chaotic systems. The
vanishing of the normalized cumulants , , implies a Gaussian
behaviour of , which is realized in the case of chaotic systems, whereas
non-chaotic systems display non-vanishing values for these cumulants leading to
a non-Gaussian behaviour of . For some integrable systems there exist
rigorous proofs of the non-Gaussian behaviour which are also discussed. Our
numerical results and the rigorous results for integrable systems suggest that
a clear fingerprint of chaotic systems is provided by a Gaussian distribution
of the mode-fluctuation distribution .Comment: 44 pages, Postscript. The figures are included in low resolution
only. A full version is available at
http://www.physik.uni-ulm.de/theo/qc/baecker.htm
Moments of Wishart-Laguerre and Jacobi ensembles of random matrices: application to the quantum transport problem in chaotic cavities
We collect explicit and user-friendly expressions for one-point densities of
the real eigenvalues of Wishart-Laguerre and Jacobi
random matrices with orthogonal, unitary and symplectic symmetry. Using these
formulae, we compute integer moments for all
symmetry classes without any large approximation. In particular, our
results provide exact expressions for moments of transmission eigenvalues in
chaotic cavities with time-reversal or spin-flip symmetry and supporting a
finite and arbitrary number of electronic channels in the two incoming leads.Comment: 27 pages, 3 figures. Typos fixed, references adde
Periodic orbit theory of strongly anomalous transport
We establish a deterministic technique to investigate transport moments of
arbitrary order. The theory is applied to the analysis of different kinds of
intermittent one-dimensional maps and the Lorentz gas with infinite horizon:
the typical appearance of phase transitions in the spectrum of transport
exponents is explained.Comment: 22 pages, 10 figures, revised versio
Thermodynamics of small Fermi systems: quantum statistical fluctuations
We investigate the probability distribution of the quantum fluctuations of
thermodynamic functions of finite, ballistic, phase-coherent Fermi gases.
Depending on the chaotic or integrable nature of the underlying classical
dynamics, on the thermodynamic function considered, and on temperature, we find
that the probability distributions are dominated either (i) by the local
fluctuations of the single-particle spectrum on the scale of the mean level
spacing, or (ii) by the long-range modulations of that spectrum produced by the
short periodic orbits. In case (i) the probability distributions are computed
using the appropriate local universality class, uncorrelated levels for
integrable systems and random matrix theory for chaotic ones. In case (ii) all
the moments of the distributions can be explicitly computed in terms of
periodic orbit theory, and are system-dependent, non-universal, functions. The
dependence on temperature and number of particles of the fluctuations is
explicitly computed in all cases, and the different relevant energy scales are
displayed.Comment: 24 pages, 7 figures, 5 table
Frequency and Phase Synchronization in Neuromagnetic Cortical Responses to Flickering-Color Stimuli
In our earlier study dealing with the analysis of neuromagnetic responses
(magnetoencephalograms - MEG) to flickering-color stimuli for a group of
control human subjects (9 volunteers) and a patient with photosensitive
epilepsy (a 12-year old girl), it was shown that Flicker-Noise Spectroscopy
(FNS) was able to identify specific differences in the responses of each
organism. The high specificity of individual MEG responses manifested itself in
the values of FNS parameters for both chaotic and resonant components of the
original signal. The present study applies the FNS cross-correlation function
to the analysis of correlations between the MEG responses simultaneously
measured at spatially separated points of the human cortex processing the
red-blue flickering color stimulus. It is shown that the cross-correlations for
control (healthy) subjects are characterized by frequency and phase
synchronization at different points of the cortex, with the dynamics of
neuromagnetic responses being determined by the low-frequency processes that
correspond to normal physiological rhythms. But for the patient, the frequency
and phase synchronization breaks down, which is associated with the suppression
of cortical regulatory functions when the flickering-color stimulus is applied,
and higher frequencies start playing the dominating role. This suggests that
the disruption of correlations in the MEG responses is the indicator of
pathological changes leading to photosensitive epilepsy, which can be used for
developing a method of diagnosing the disease based on the analysis with the
FNS cross-correlation function.Comment: 21 pages, 14 figures; submitted to "Laser Physics", 2010, 2
Semiclassical Trace Formulae and Eigenvalue Statistics in Quantum Chaos
A detailed discussion of semiclassical trace formulae is presented and it is
demonstrated how a regularized trace formula can be derived while dealing only
with finite and convergent expressions. Furthermore, several applications of
trace formula techniques to quantum chaos are reviewed. Then local spectral
statistics, measuring correlations among finitely many eigenvalues, are
reviewed and a detailed semiclassical analysis of the number variance is given.
Thereafter the transition to global spectral statistics, taking correlations
among infinitely many quantum energies into account, is discussed. It is
emphasized that the resulting limit distributions depend on the way one passes
to the global scale. A conjecture on the distribution of the fluctuations of
the spectral staircase is explained in this general context and evidence
supporting the conjecture is discussed.Comment: 48 pages, LaTeX, uses amssym
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