On the diffusive anomalies in a long-range Hamiltonian system

We scrutinize the anomalies in diffusion observed in an extended long-range system of classical rotors, the HMF model. Under suitable preparation, the system falls into long-lived quasi-stationary states presenting super-diffusion of rotor phases. We investigate the diffusive motion of phases by monitoring the evolution of their probability density function for large system sizes. These densities are shown to be of the $q$-Gaussian form, $P(x)\propto (1+(q-1)[x/\beta]^2)^{1/(1-q)}$, with parameter $q$ increasing with time before reaching a steady value $q\simeq 3/2$. From this perspective, we also discuss the relaxation to equilibrium and show that diffusive motion in quasi-stationary trajectories strongly depends on system size.Comment: 5 pages, 5 figures. References added and correcte

Observability and Synchronization of Neuron Models

Observability is the property that enables to distinguish two different locations in $n$-dimensional state space from a reduced number of measured variables, usually just one. In high-dimensional systems it is therefore important to make sure that the variable recorded to perform the analysis conveys good observability of the system dynamics. In the case of networks composed of neuron models, the observability of the network depends nontrivially on the observability of the node dynamics and on the topology of the network. The aim of this paper is twofold. First, a study of observability is conducted using four well-known neuron models by computing three different observability coefficients. This not only clarifies observability properties of the models but also shows the limitations of applicability of each type of coefficients in the context of such models. Second, a multivariate singular spectrum analysis (M-SSA) is performed to detect phase synchronization in networks composed by neuron models. This tool, to the best of the authors' knowledge has not been used in the context of networks of neuron models. It is shown that it is possible to detect phase synchronization i)~without having to measure all the state variables, but only one from each node, and ii)~without having to estimate the phase

Topological features of hydrogenated graphene

Hydrogen adatoms are one of the most the promising proposals for the functionalization of graphene. Hydrogen induces narrow resonances near the Dirac energy, which lead to the formation of magnetic moments. Furthermore, they also create local lattice distortions which enhance the spin-orbit coupling. The combination of magnetism and spin-orbit coupling allows for a rich variety of phases, some of which have non trivial topological features. We analyze the interplay between magnetism and spin-orbit coupling in ordered arrays of hydrogen on graphene monolayers, and classify the different phases that may arise. We extend our model to consider arrays of adsorbates in graphene-like crystals with stronger intrinsic spin-orbit couplings.Comment: 6 pages, 4 figure

Particle Physics on Ice: Constraints on Neutrino Interactions Far Above the Weak Scale

Ultra-high energy cosmic rays and neutrinos probe energies far above the weak scale. Their usefulness might appear to be limited by astrophysical uncertainties; however, by simultaneously considering up- and down-going events, one may disentangle particle physics from astrophysics. We show that present data from the AMANDA experiment in the South Pole ice already imply an upper bound on neutrino cross sections at energy scales that will likely never be probed at man-made accelerators. The existing data also place an upper limit on the neutrino flux valid for any neutrino cross section. In the future, similar analyses of IceCube data will constrain neutrino properties and fluxes at the O(10%) level.Comment: 4 pages, 1 figure, published versio

Quantum phases of a qutrit

We consider various approaches to treat the phases of a qutrit. Although it is possible to represent qutrits in a convenient geometrical manner by resorting to a generalization of the Poincare sphere, we argue that the appropriate way of dealing with this problem is through phase operators associated with the algebra su(3). The rather unusual properties of these phases are caused by the small dimension of the system and are explored in detail. We also examine the positive operator-valued measures that can describe the qutrit phase properties.Comment: 6 page

Classical Radiation Reaction in Particle-In-Cell Simulations

Under the presence of ultra high intensity lasers or other intense electromagnetic fields the motion of particles in the ultrarelativistic regime can be severely affected by radiation reaction. The standard particle-in-cell (PIC) algorithms do not include radiation reaction effects. Even though this is a well known mechanism, there is not yet a definite algorithm nor a standard technique to include radiation reaction in PIC codes. We have compared several models for the calculation of the radiation reaction force, with the goal of implementing an algorithm for classical radiation reaction in the Osiris framework, a state-of-the-art PIC code. The results of the different models are compared with standard analytical results, and the relevance/advantages of each model are discussed. Numerical issues relevant to PIC codes such as resolution requirements, application of radiation reaction to macro particles and computational cost are also addressed. The Landau and Lifshitz reduced model is chosen for implementation.Comment: 12 pages, 8 figure