585 research outputs found
Statistics of extinction and survival in Lotka-Volterra systems
We analyze purely competitive many-species Lotka-Volterra systems with random
interaction matrices, focusing the attention on statistical properties of their
asymptotic states. Generic features of the evolution are outlined from a
semiquantitative analysis of the phase-space structure, and extensive numerical
simulations are performed to study the statistics of the extinctions. We find
that the number of surviving species depends strongly on the statistical
properties of the interaction matrix, and that the probability of survival is
weakly correlated to specific initial conditions.Comment: Previous version had error in authors. 11 pages, including 5 figure
Statistics of Wave Functions in Coupled Chaotic Systems
Using the supersymmetry technique, we calculate the joint distribution of
local densities of electron wavefunctions in two coupled disordered or chaotic
quantum billiards. We find novel spatial correlations that are absent in a
single chaotic system. Our exact result can be interpreted for small coupling
in terms of the hybridization of eigenstates of the isolated billiards. We show
that the presented picture is universal, independent of microscopic details of
the coupling.Comment: 4 pages, 2 figures; acknowledgements and references adde
Combining a disease model with a crop phenology model to assess and map pest risk: Karnal bunt disease (Tilletia indica) of wheat in Europe
Level-Spacing Distributions and the Bessel Kernel
The level spacing distributions which arise when one rescales the Laguerre or
Jacobi ensembles of hermitian matrices is studied. These distributions are
expressible in terms of a Fredholm determinant of an integral operator whose
kernel is expressible in terms of Bessel functions of order . We derive
a system of partial differential equations associated with the logarithmic
derivative of this Fredholm determinant when the underlying domain is a union
of intervals. In the case of a single interval this Fredholm determinant is a
Painleve tau function.Comment: 18 pages, resubmitted to make postscript compatible, no changes to
manuscript conten
Level Spacing Distribution of Critical Random Matrix Ensembles
We consider unitary invariant random matrix ensembles which obey spectral
statistics different from the Wigner-Dyson, including unitary ensembles with
slowly (~(log x)^2) growing potentials and the finite-temperature fermi gas
model. If the deformation parameters in these matrix ensembles are small, the
asymptotically translational-invariant region in the spectral bulk is
universally governed by a one-parameter generalization of the sine kernel. We
provide an analytic expression for the distribution of the eigenvalue spacings
of this universal asymptotic kernel, which is a hybrid of the Wigner-Dyson and
the Poisson distributions, by determining the Fredholm determinant of the
universal kernel in terms of a Painleve VI transcendental function.Comment: 5 pages, 1 figure, REVTeX; restriction on the parameter stressed,
figure replaced, refs added (v2); typos (factors of pi) in (35), (36)
corrected (v3); minor changes incl. title, version to appear in Phys.Rev.E
(v4
Fredholm Determinants, Differential Equations and Matrix Models
Orthogonal polynomial random matrix models of NxN hermitian matrices lead to
Fredholm determinants of integral operators with kernel of the form (phi(x)
psi(y) - psi(x) phi(y))/x-y. This paper is concerned with the Fredholm
determinants of integral operators having kernel of this form and where the
underlying set is a union of open intervals. The emphasis is on the
determinants thought of as functions of the end-points of these intervals. We
show that these Fredholm determinants with kernels of the general form
described above are expressible in terms of solutions of systems of PDE's as
long as phi and psi satisfy a certain type of differentiation formula. There is
also an exponential variant of this analysis which includes the circular
ensembles of NxN unitary matrices.Comment: 34 pages, LaTeX using RevTeX 3.0 macros; last version changes only
the abstract and decreases length of typeset versio
Scaling Analysis of Fluctuating Strength Function
We propose a new method to analyze fluctuations in the strength function
phenomena in highly excited nuclei. Extending the method of multifractal
analysis to the cases where the strength fluctuations do not obey power scaling
laws, we introduce a new measure of fluctuation, called the local scaling
dimension, which characterizes scaling behavior of the strength fluctuation as
a function of energy bin width subdividing the strength function. We discuss
properties of the new measure by applying it to a model system which simulates
the doorway damping mechanism of giant resonances. It is found that the local
scaling dimension characterizes well fluctuations and their energy scales of
fine structures in the strength function associated with the damped collective
motions.Comment: 22 pages with 9 figures; submitted to Phys. Rev.
Chaos Driven Decay of Nuclear Giant Resonances: Route to Quantum Self-Organization
The influence of background states with increasing level of complexity on the
strength distribution of the isoscalar and isovector giant quadrupole resonance
in Ca is studied. It is found that the background characteristics,
typical for chaotic systems, strongly affects the fluctuation properties of the
strength distribution. In particular, the small components of the wave function
obey a scaling law analogous to self-organized systems at the critical state.
This appears to be consistent with the Porter-Thomas distribution of the
transition strength.Comment: 14 pages, 4 Figures, Illinois preprint P-93-12-106, Figures available
from the author
Sublocalization, superlocalization, and violation of standard single parameter scaling in the Anderson model
We discuss the localization behavior of localized electronic wave functions
in the one- and two-dimensional tight-binding Anderson model with diagonal
disorder. We find that the distributions of the local wave function amplitudes
at fixed distances from the localization center are well approximated by
log-normal fits which become exact at large distances. These fits are
consistent with the standard single parameter scaling theory for the Anderson
model in 1d, but they suggest that a second parameter is required to describe
the scaling behavior of the amplitude fluctuations in 2d. From the log-normal
distributions we calculate analytically the decay of the mean wave functions.
For short distances from the localization center we find stretched exponential
localization ("sublocalization") in both, 1d and 2d. In 1d, for large
distances, the mean wave functions depend on the number of configurations N
used in the averaging procedure and decay faster that exponentially
("superlocalization") converging to simple exponential behavior only in the
asymptotic limit. In 2d, in contrast, the localization length increases
logarithmically with the distance from the localization center and
sublocalization occurs also in the second regime. The N-dependence of the mean
wave functions is weak. The analytical result agrees remarkably well with the
numerical calculations.Comment: 12 pages with 9 figures and 1 tabl
Collectivity Embedded in Complex Spectra of Finite Interacting Fermi Systems: Nuclear Example
The mechanism of collectivity coexisting with chaos in a finite system of
strongly interacting fermions is investigated. The complex spectra are
represented in the basis of two-particle two-hole states describing the nuclear
double-charge exchange modes in Ca. An example of
excitations shows that the residual interaction, which generically implies
chaotic behavior, under certain specific and well identified conditions may
create strong transitions, even much stronger than those corresponding to a
pure mean-field picture. Such an effect results from correlations among the
off-diagonal matrix elements, is connected with locally reduced density of
states and a local minimum in the information entropy.Comment: 16 pages, LaTeX2e, REVTeX, 8 PostScript figures, to appear in
Physical Review
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