2,606 research outputs found
Long-range epidemic spreading in a random environment
Modeling long-range epidemic spreading in a random environment, we consider a
quenched disordered, -dimensional contact process with infection rates
decaying with the distance as . We study the dynamical behavior
of the model at and below the epidemic threshold by a variant of the
strong-disorder renormalization group method and by Monte Carlo simulations in
one and two spatial dimensions. Starting from a single infected site, the
average survival probability is found to decay as up to
multiplicative logarithmic corrections. Below the epidemic threshold, a
Griffiths phase emerges, where the dynamical exponent varies continuously
with the control parameter and tends to as the threshold is
approached. At the threshold, the spatial extension of the infected cluster (in
surviving trials) is found to grow as with a
multiplicative logarithmic correction, and the average number of infected sites
in surviving trials is found to increase as with
in one dimension.Comment: 12 pages, 6 figure
Description of two-electron atoms with correct cusp conditions
New sets of functions with arbitrary large finite cardinality are constructed
for two-electron atoms. Functions from these sets exactly satisfy the Kato's
cusp conditions. The new functions are special linear combinations of
Hylleraas- and/or Kinoshita-type terms. Standard variational calculation,
leading to matrix eigenvalue problem, can be carried out to calculate the
energies of the system. There is no need for optimization with constraints to
satisfy the cusp conditions. In the numerical examples the ground state energy
of the He atom is considered
Anderson transition and multifractals in the spectrum of the Dirac operator of Quantum Chromodynamics at high temperature
We investigate the Anderson transition found in the spectrum of the Dirac
operator of Quantum Chromodynamics (QCD) at high temperature, studying the
properties of the critical quark eigenfunctions. Applying multifractal
finite-size scaling we determine the critical point and the critical exponent
of the transition, finding agreement with previous results, and with available
results for the unitary Anderson model. We estimate several multifractal
exponents, finding also in this case agreement with a recent determination for
the unitary Anderson model. Our results confirm the presence of a true Anderson
localization-delocalization transition in the spectrum of the quark Dirac
operator at high-temperature, and further support that it belongs to the 3D
unitary Anderson model class.Comment: 10 pages, 6 figure
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