129 research outputs found
Topology invariance in Percolation Thresholds
An universal invariant for site and bond percolation thresholds (p_{cs} and
p_{cb} respectively) is proposed. The invariant writes
{p_{cs}}^{1/a_s}{p_{cb}}^{-1/a_b}=\delta/d where a_s, a_b and \delta are
positive constants,and d the space dimension. It is independent of the
coordination number, thus exhibiting a topology invariance at any d.The formula
is checked against a large class of percolation problems, including percolation
in non-Bravais lattices and in aperiodic lattices as well as rigid percolation.
The invariant is satisfied within a relative error of \pm 5% for all the twenty
lattices of our sample at d=2, d=3, plus all hypercubes up to d=6.Comment: 11 pages, latex, 1 figure include
Cooper pairs without 'glue' in high- superconductors
We address the origin of the Cooper pairs in high- cuprates and the
unique nature of the superconducting (SC) condensate. Itinerant holes in an
antiferromagnetic background form pairs spontaneously, without any `glue',
defining a new quantum object the `pairon'. In the incoherent pseudogap phase,
above or within the vortex core, the pairon binding energies are
distributed statistically, forming a `Cooper-pair glass'. Contrary to
conventional SC, it is the mutual pair-pair interaction that is responsable for
the condensation. We give a natural explanation for the {\it ergodic rigidity}
of the excitation gap, being uniquely determined by the carrier concentration
and . The phase diagram can be understood, without spin fluctuations, in
terms of a single energy scale , the exchange energy at the
metal-insulator transition
Anomalous diffusion of a particle in an aging medium
We report new results about the anomalous diffusion of a particle in an aging
medium. For each given age, the quasi-stationary particle velocity is governed
by a generalized Langevin equation with a frequency-dependent friction
coefficient proportional to at small frequencies, with
. The aging properties of the medium are encoded in a frequency
dependent effective temperature . The latter is modelized
by a function proportional to at small frequencies, with
, thus allowing for the medium to have a density of slow modes
proportionally larger than in a thermal bath. Using asymptotic Fourier
analysis, we obtain the behaviour at large times of the velocity correlation
function and of the mean square displacement. As a result, the anomalous
diffusion exponent in the aging medium appears to be linked, not only to
as it would be the case in a thermal bath, but also to the exponent
characterizing the density of slow modes
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