15 research outputs found
Statistical Properties of Cross-Correlation in the Korean Stock Market
We investigate the statistical properties of the correlation matrix between
individual stocks traded in the Korean stock market using the random matrix
theory (RMT) and observe how these affect the portfolio weights in the
Markowitz portfolio theory. We find that the distribution of the correlation
matrix is positively skewed and changes over time. We find that the eigenvalue
distribution of original correlation matrix deviates from the eigenvalues
predicted by the RMT, and the largest eigenvalue is 52 times larger than the
maximum value among the eigenvalues predicted by the RMT. The
coefficient, which reflect the largest eigenvalue property, is 0.8, while one
of the eigenvalues in the RMT is approximately zero. Notably, we show that the
entropy function with the portfolio risk for the original
and filtered correlation matrices are consistent with a power-law function,
, with the exponent and
those for Asian currency crisis decreases significantly
Exact Study of the Effect of Level Statistics in Ultrasmall Superconducting Grains
The reduced BCS model that is commonly used for ultrasmall superconducting
grains has an exact solution worked out long ago by Richardson in the context
of nuclear physics. We use it to check the quality of previous treatments of
this model, and to investigate the effect of level statistics on pairing
correlations. We find that the ground state energies are on average somewhat
lower for systems with non-uniform than uniform level spacings, but both have
an equally smooth crossover from the bulk to the few-electron regime. In the
latter, statistical fluctuations in ground state energies strongly depend on
the grain's electron number parity.Comment: 4 pages, 3 eps figs, RevTe
Scattering phases in quantum dots: an analysis based on lattice models
The properties of scattering phases in quantum dots are analyzed with the
help of lattice models. We first derive the expressions relating the different
scattering phases and the dot Green functions. We analyze in detail the Friedel
sum rule and discuss the deviation of the phase of the transmission amplitude
from the Friedel phase at the zeroes of the transmission. The occurrence of
such zeroes is related to the parity of the isolated dot levels. A statistical
analysis of the isolated dot wave-functions reveals the absence of significant
correlations in the parity for large disorder and the appearance, for weak
disorder, of certain dot states which are strongly coupled to the leads. It is
shown that large differences in the coupling to the leads give rise to an
anomalous charging of the dot levels. A mechanism for the phase lapse observed
experimentally based on this property is discussed and illustrated with model
calculations.Comment: 18 pages, 9 figures. to appear in Physical Review
Evolution of wave packets in quasi-1D and 1D random media: diffusion versus localization
We study numerically the evolution of wavepackets in quasi one-dimensional
random systems described by a tight-binding Hamiltonian with long-range random
interactions. Results are presented for the scaling properties of the width of
packets in three time regimes: ballistic, diffusive and localized. Particular
attention is given to the fluctuations of packet widths in both the diffusive
and localized regime. Scaling properties of the steady-state distribution are
also analyzed and compared with theoretical expression borrowed from
one-dimensional Anderson theory. Analogies and differences with the kicked
rotator model and the one-dimensional localization are discussed.Comment: 32 pages, LaTex, 11 PostScript figure
Self-sorting of porous Cu(4)L(2)L'(2) metal-organic cages composed of isomerisable ligands
We report the self-sorting of a dynamic combinatorial library (DCL) of metal–organic cages composed of a rotationally isomerisable ligand. Convergence of the DCL occurs upon crystallisation and leads to low-symmetry Cu₄L₂L′₂ cages that display differing porosities based on their overall shape and ligand configuration.Adrian W. Markwell-Heys, Matthew L. Schneider, Jenica Marie L. Madridejos, Gregory F. Metha and Witold M. Bloc