Phase transition for the frog model

We study a system of simple random walks on graphs, known as frog model. This model can be described as follows: There are active and sleeping particles living on some graph G. Each active particle performs a simple random walk with discrete time and at each moment it may disappear with probability 1-p. When an active particle hits a sleeping particle, the latter becomes active. Phase transition results and asymptotic values for critical parameters are presented for Z^d and regular trees

Coulomb corrections to inclusive cross sections at the future Electron - Ion Collider

The experimental results of the future electron -- ion ($e A$) collider are expected to constrain the dynamics of the strong interactions at small values of the Bjorken -- $x$ variable and large nuclei. Recently it has been suggested that Coulomb corrections can be important in inclusive and diffractive $eA$ interactions. In this paper we present a detailed investigation of the impact of the Coulomb corrections to some of the observables that will be measured in the future $eA$ collider. In particular, we estimate the magnitude of these corrections for the charm and longitudinal cross sections in inclusive and diffractive interactions. Our results demonstrate that the Coulomb corrections for these observables are negligible, which implies that they can be used to probe the QCD dynamics.Comment: 9 pages, 6 figures. Improved version to be published in Physical Review

The graphene sheet versus the 2DEG: a relativistic Fano spin-filter via STM and AFM tips

We explore theoretically the density of states (LDOS) probed by an STM tip of 2D systems hosting an adatom and a subsurface impurity,both capacitively coupled to AFM tips and traversed by antiparallel magnetic fields. Two kinds of setups are analyzed, a monolayer of graphene and a two-dimensional electron gas (2DEG). The AFM tips set the impurity levels at the Fermi energy, where two contrasting behaviors emerge: the Fano factor for the graphene diverges, while in the 2DEG it approaches zero. As result, the spin-degeneracy of the LDOS is lifted exclusively in the graphene system, in particular for the asymmetric regime of Fano interference. The aftermath of this limit is a counterintuitive phenomenon, which consists of a dominant Fano factor due to the subsurface impurity even with a stronger STM-adatom coupling. Thus we find a full polarized conductance, achievable just by displacing vertically the position of the STM tip. To the best knowledge, our work is the first to propose the Fano effect as the mechanism to filter spins in graphene. This feature arises from the massless Dirac electrons within the band structure and allows us to employ the graphene host as a relativistic Fano spin-filter