37,430 research outputs found
Scaling behavior of explosive percolation on the square lattice
Clusters generated by the product-rule growth model of Achlioptas, D'Souza,
and Spencer on a two-dimensional square lattice are shown to obey qualitatively
different scaling behavior than standard (random growth) percolation. The
threshold with unrestricted bond placement (allowing loops) is found precisely
using several different criteria based upon both moments and wrapping
probabilities, yielding p_c = 0.526565 +/- 0.000005, consistent with the recent
result of Radicchi and Fortunato. The correlation-length exponent nu is found
to be close to 1. The qualitative difference from regular percolation is shown
dramatically in the behavior of the percolation probability P_(infinity) (size
of largest cluster), the susceptibility, and of the second moment of finite
clusters, where discontinuities appears at the threshold. The critical
cluster-size distribution does not follow a consistent power-law for the range
of system sizes we study L 2
for larger L.Comment: v2: Updated results in original version with new data; expanded
discussion. v3: Resubmitted version. New figures, reference
Hermitian Dirac Hamiltonian in time dependent gravitational field
It is shown by a straightforward argument that the Hamiltonian generating the
time evolution of the Dirac wave function in relativistic quantum mechanics is
not hermitian with respect to the covariantly defined inner product whenever
the background metric is time dependent. An alternative, hermitian, Hamiltonian
is found and is shown to be directly related to the canonical field Hamiltonian
used in quantum field theory.Comment: 9 pages, final version, to appear in Class. Quant. Gra
Treatment of the infrared contribution: NLO QED evolution as a pedagogic example
We show that the conventional prescription used for DGLAP parton evolution at
NLO has an inconsistent treatment of the contribution from the infrared (IR)
region. We illustrate the problem by studying the simple example of QED
evolution, treating the electron and photon as partons. The deficiency is not
present in a physical approach which removes the IR divergency and allows
calculation in the normal 4-dimensional space.Comment: 15 pages, 2 figures, erratum at the end of the articl
Corrections to Finite Size Scaling in Percolation
A 1/L-expansion for percolation problems is proposed, where L is the lattice
finite length. The square lattice with 27 different sizes L = 18, 22 ... 1594
is considered. Certain spanning probabilities were determined by Monte Carlo
simulations, as continuous functions of the site occupation probability p. We
estimate the critical threshold pc by applying the quoted expansion to these
data. Also, the universal spanning probability at pc for an annulus with aspect
ratio r=1/2 is estimated as C = 0.876657(45)
Improving the Drell-Yan probe of small x partons at the LHC via a k_t cut
We show that the observation of the Drell-Yan production of low-mass
lepton-pairs (M 3) at the LHC can make a
direct measurement of parton distribution functions (PDFs) in the low x region,
x < 10^{-4}. We describe a procedure that greatly reduces the sensitivity of
the predictions to the choice of the factorization scale and, in particular,
show how, by imposing a cutoff on the transverse momentum of the lepton-pair,
the data are able to probe PDFs in the important low scale, low x domain. We
include the effects of the Sudakov suppression factor.Comment: 14 pages, 5 figures, version to be published in EPJC, with expanded
explanatio
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