61,038 research outputs found
The phase diagram of the multi-dimensional Anderson localization via analytic determination of Lyapunov exponents
The method proposed by the present authors to deal analytically with the
problem of Anderson localization via disorder [J.Phys.: Condens. Matter {\bf
14} (2002) 13777] is generalized for higher spatial dimensions D. In this way
the generalized Lyapunov exponents for diagonal correlators of the wave
function, , can be calculated analytically and
exactly. This permits to determine the phase diagram of the system. For all
dimensions one finds intervals in the energy and the disorder where
extended and localized states coexist: the metal-insulator transition should
thus be interpreted as a first-order transition. The qualitative differences
permit to group the systems into two classes: low-dimensional systems (), where localized states are always exponentially localized and
high-dimensional systems (), where states with non-exponential
localization are also formed. The value of the upper critical dimension is
found to be for the Anderson localization problem; this value is also
characteristic of a related problem - percolation.Comment: 17 pages, 5 figures, to appear in Eur. Phys.J.
Disorder effects on the static scattering function of star branched polymers
We present an analysis of the impact of structural disorder on the static
scattering function of f-armed star branched polymers in d dimensions. To this
end, we consider the model of a star polymer immersed in a good solvent in the
presence of structural defects, correlated at large distances r according to a
power law \sim r^{-a}. In particular, we are interested in the ratio g(f) of
the radii of gyration of star and linear polymers of the same molecular weight,
which is a universal experimentally measurable quantity. We apply a direct
polymer renormalization approach and evaluate the results within the double
\varepsilon=4-d, \delta=4-a-expansion. We find an increase of g(f) with an
increasing \delta. Therefore, an increase of disorder correlations leads to an
increase of the size measure of a star relative to linear polymers of the same
molecular weight.Comment: 17 pages, 7 figure
Microscopic analysis of K^+-nucleus elastic scattering based on K^+N phase shifts
We investigate -nucleus elastic scattering at intermediate energies
within a microscopic optical model approach. To this effect we use the current
-nucleon {\it (KN)} phase shifts from the Center for Nuclear Studies of
the George Washington University as primary input. First, the {\it KN} phase
shifts are used to generate Gel'fand-Levitan-Marchenko real and local inversion
potentials. Secondly, these potentials are supplemented with a short range
complex separable term in such a way that the corresponding unitary and
non-unitary {\it KN} matrices are exactly reproduced. These {\it KN}
potentials allow to calculate all needed on- and off-shell contributions of the
matrix,the driving effective interaction in the full-folding
-nucleus optical model potentials reported here. Elastic scattering of
positive kaons from Li, C, Si and Ca are studied at
beam momenta in the range 400-1000 MeV/{}, leading to a fair description of
most differential and total cross section data. To complete the analysis the
full-folding model, three kinds of simpler calculations are considered
and results discussed. We conclude that conventional medium effects, in
conjunction with a proper representation of the basic {\it KN} interaction are
essential for the description of -nucleus phenomena.Comment: 11 pages, 1 table, 12 figures, submitted to PR
Scaling in public transport networks
We analyse the statistical properties of public transport networks. These
networks are defined by a set of public transport routes (bus lines) and the
stations serviced by these. For larger networks these appear to possess a
scale-free structure, as it is demonstrated e.g. by the Zipf law distribution
of the number of routes servicing a given station or for the distribution of
the number of stations which can be visited from the chosen one without
changing the means of transport. Moreover, a rather particular feature of the
public transport network is that many routes service common subsets of
stations. We discuss the possibility of new scaling laws that govern intrinsic
features of such subsets.Comment: 9 pages, 4 figure
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