Information entropy of classical versus explosive percolation

We study the Shannon entropy of the cluster size distribution in classical as well as explosive percolation, in order to estimate the uncertainty in the sizes of randomly chosen clusters. At the critical point the cluster size distribution is a power-law, i.e. there are clusters of all sizes, so one expects the information entropy to attain a maximum. As expected, our results show that the entropy attains a maximum at this point for classical percolation. Surprisingly, for explosive percolation the maximum entropy does not match the critical point. Moreover, we show that it is possible determine the critical point without using the conventional order parameter, just analysing the entropy's derivatives.Comment: 6 pages, 6 figure

A simple deterministic self-organized critical system

We introduce a new continuous cellular automaton that presents self-organized criticality. It is one-dimensional, totally deterministic, without any kind of embedded randomness, not even in the initial conditions. This system is in the same universality class as the Oslo rice pile system, boundary driven interface depinning and the train model for earthquakes. Although the system is chaotic, in the thermodynamic limit chaos occurs only in a microscopic level.Comment: System slightly modified. New results on Liapunov exponents. Submitted for publication (8 pages

Electron Fabry-Perot interferometer with two entangled magnetic impurities

We consider a one-dimensional (1D) wire along which single conduction electrons can propagate in the presence of two spin-1/2 magnetic impurities. The electron may be scattered by each impurity via a contact-exchange interaction and thus a spin-flip generally occurs at each scattering event. Adopting a quantum waveguide theory approach, we derive the stationary states of the system at all orders in the electron-impurity exchange coupling constant. This allows us to investigate electron transmission for arbitrary initial states of the two impurity spins. We show that for suitable electron wave vectors, the triplet and singlet maximally entangled spin states of the impurities can respectively largely inhibit the electron transport or make the wire completely transparent for any electron spin state. In the latter case, a resonance condition can always be found, representing an anomalous behaviour compared to typical decoherence induced by magnetic impurities. We provide an explanation for these phenomena in terms of the Hamiltonian symmetries. Finally, a scheme to generate maximally entangled spin states of the two impurities via electron scattering is proposed.Comment: 19 page

Evaluation of the ground surface Enthalpy balance from bedrock shallow borehole temperatures (Livingston Island, Maritime Antarctic)

International audienceThe annual evolution of the ground temperatures from Incinerador borehole in Livingston Island (South Shetlands, Antarctic) is studied. The borehole is 2.4 m deep and is located in a quartzite outcrop in the proximity of the Spanish Antarctic Station Juan Carlos I. In order to model the movement of the 0°C isotherm (velocity and maximum depth) hourly temperature profiles from: (i) the cooling periods of the frost seasons of 2000 to 2005, and (ii) the warming periods of the thaw seasons of 2002?2003, 2003?2004 and 2004?2005, were studied. In this modelling approach, heat gains and losses across ground surface are considered to be the causes for the 0°C isotherm movement. A methodological approach to calculate the Enthalpy change based on the thermodynamic analysis of the ground during the cooling and warming periods is proposed. The Enthalpy change is equivalent to the heat exchange through the ground surface during each season, thus enabling to describe the interaction ground-atmosphere and providing valuable data for studies on permafrost and periglacial processes. The bedrock density is considered to be constant in the borehole and initial isothermal conditions at 0°C are assumed to run the model. The final stages correspond to the temperatures at the end of the cooling and warming periods (annual minima and maxima)

Chaos and Synchronized Chaos in an Earthquake Model

We show that chaos is present in the symmetric two-block Burridge-Knopoff model for earthquakes. This is in contrast with previous numerical studies, but in agreement with experimental results. In this system, we have found a rich dynamical behavior with an unusual route to chaos. In the three-block system, we see the appearance of synchronized chaos, showing that this concept can have potential applications in the field of seismology.Comment: To appear in Physical Review Letters (13 pages, 6 figures

Self-Similarity of Friction Laws

The change of the friction law from a mesoscopic level to a macroscopic level is studied in the spring-block models introduced by Burridge-Knopoff. We find that the Coulomb law is always scale invariant. Other proposed scaling laws are only invariant under certain conditions.}Comment: Plain TEX. Figures not include

Point-contact spectroscopy on URu2_2Si2_2

Tunnel and point contact experiments have been made in a URu$_2$Si$_2$ single crystal along the c-axis. The experiments were performed changing temperature and contact size in a low temperature scanning tunneling microscope. A resonance develops at the Fermi level at $T\sim 60$ K. This resonance splits and becomes asymmetric when the 17.5 K phase transition is crossed. These results are consistent with the existence of Kondo like bound states of the U$^{4+}$ ionic configurations and the conduction electrons. Below the transition, these configurations are split by the development of quadrupolar ordering. The peak separation can be interpreted as a direct measurement of the order parameter. Measurements on a policrystalline UAu_2Si_2$ sample are also reported, with a comparative study of the behavior of both materials.Comment: 4 pages (Latex) + 2 postscript figure