1,732 research outputs found

### Growing Cayley trees described by Fermi distribution

We introduce a model for growing Cayley trees with thermal noise. The
evolution of these hierarchical networks reduces to the Eden model and the
Invasion Percolation model in the limit $T\to 0$, $T\to \infty$ respectively.
We show that the distribution of the bond strengths (energies) is described by
the Fermi statistics. We discuss the relation of the present results with the
scale-free networks described by Bose statistics

### Multiband superconductors close to a 3D-2D electronic topological transition

Within the two-band model of superconductivity, we study the dependence of
the critical temperature Tc and of the isotope exponent alpha in the proximity
to an electronic topological transition (ETT). The ETT is associated with a
3D-2D crossover of the Fermi surface of one of the two bands: the sigma subband
of the diborides. Our results agree with the observed dependence of Tc on Mg
content in A_{1-x}Mg_xB_2 (A=Al or Sc), where an enhancement of Tc can be
interpreted as due to the proximity to a "shape resonance". Moreover we have
calculated a possible variation of the isotope effect on the superconducting
critical temperature by tuning the chemical potential.Comment: J. Supercond., to appea

### Rare events and discontinuous percolation transitions

Percolation theory characterizing the robustness of a network has
applications ranging from biology, to epidemic spreading, and complex
infrastructures. Percolation theory, however, only concern the typical response
of a infinite network to random damage of its nodes while in real finite
networks, fluctuations are observable. Consequently for finite networks there
is an urgent need to evaluate the risk of collapse in response to rare
configurations of the initial damage. Here we build a large deviation theory of
percolation characterizing the response of a sparse network to rare events.
This general theory includes the second order phase transition observed
typically for random configurations of the initial damage but reveals also
discontinuous transitions corresponding to rare configurations of the initial
damage for which the size of the giant component is suppressed.Comment: (11 pages, 4 figures

### Effects of azimuth-symmetric acceptance cutoffs on the measured asymmetry in unpolarized Drell-Yan fixed target experiments

Fixed-target unpolarized Drell-Yan experiments often feature an acceptance
depending on the polar angle of the lepton tracks in the laboratory frame.
Typically leptons are detected in a defined angular range, with a dead zone in
the forward region. If the cutoffs imposed by the angular acceptance are
independent of the azimuth, at first sight they do not appear dangerous for a
measurement of the cos(2\phi)-asymmetry, relevant because of its association
with the violation of the Lam-Tung rule and with the Boer-Mulders function. On
the contrary, direct simulations show that up to 10 percent asymmetries are
produced by these cutoffs. These artificial asymmetries present qualitative
features that allow them to mimic the physical ones. They introduce some
model-dependence in the measurements of the cos(2\phi)-asymmetry, since a
precise reconstruction of the acceptance in the Collins-Soper frame requires a
Monte Carlo simulation, that in turn requires some detailed physical input to
generate event distributions. Although experiments in the eighties seem to have
been aware of this problem, the possibility of using the Boer-Mulders function
as an input parameter in the extraction of Transversity has much increased the
requirements of precision on this measurement. Our simulations show that the
safest approach to these measurements is a strong cutoff on the Collins-Soper
polar angle. This reduces statistics, but does not necessarily decrease the
precision in a measurement of the Boer-Mulders function.Comment: 13 pages, 14 figure

### A Superconductor Made by a Metal Heterostructure at the Atomic Limit Tuned at the "Shape Resonance": MgB2

We have studied the variation of Tc with charge density and lattice
parameters in Mg1-xAlxB2 superconducting samples at low Al doping x<8%. We show
that high Tc occurs where the chemical potential is tuned at a "superconducting
shape resonance" near the energy Ec of the quantum critical point (QCP) for the
dimensional transition from 2D to 3D electronic structure in a particular
subband of the natural superlattice of metallic atomic boron layers. At the
"shape resonance" the electrons pairs see a 2D Fermi surface at EF-w0 and a 3D
Fermi surface at EF+wo, where wo is the energy cut off of the pairing
interaction. The resonant amplification occurs in a narrow energy range where
EF-Ec is in the range of 2wo.Comment: 16 page

- â€¦