When studying the encounter of two random walkers, in principle one can map the problem into a one particle problem, where encountering corresponds to reaching a given (set of) point(s). This mapping preserves the underlying topology as long as one focuses on infinite homogeneous structures. However, for inhomogeneous structures this is no longer the case and the new embedding topology may be extremely different. Here this peculiar feature is analyzed for the two-particle problem defined on combs which is mapped into a one-particle problem defined on book graphs. Through this mapping we can prove the emergence of the finite collision property and extend it to the case of particles with any, strictly positive, velocities \(v_1,v_2>0\). Combs obtained by using as a base self-similar fractals as well as \(d\)-dimensional combs are also considered showing that the finite collision property is robust. Finally, the mapping introduced here allows to get some insights in the finite-size problem, where encounters are also known to be slow.

Self-organized quasi periodicity is one of the most puzzling dynamical phases observed in systems of non linear coupled oscillators, as the single dynamical units are not locked to the periodic mean field they produce, but they still feature a coherent behavior. We consider a class of leaky integrate- and-fire oscillators on random sparse and massive networks with dynamical synapses featuring self- organized quasi periodicity and we show how complex collective oscillations arise from microscopic dynamics. In particular, we find a simple quantitative relationship between two relevant microscopic dynamical time scales and the macroscopic time scale of the global signal. We show that the proposed relation is a general property of collective oscillations, common to all the partially synchronous dynamical phases analyzed. We argue that an analogous mechanism could be at the origin of similar network dynamics.

A novel class of nonequilibrium phase-transitions at zero temperature is found in chains of nonlinear oscillators. For two paradigmatic systems, the Hamiltonian XY model and the discrete nonlinear Schroedinger equation, we find that the application of boundary forces induces two synchronized phases, separated by a non-trivial interfacial region where the kinetic temperature is finite. Dynamics in such supercritical state displays anomalous chaotic properties whereby some observables are non-extensive and transport is superdiffusive. At finite temperatures, the transition is smoothed out, but it still induces peculiar properties such as a non-monotonous temperature-profile in the presence of equal-temperature heat baths.

We propose 2D and 3D models for deep-seated landslide triggered by rainfall. Our models are based on interacting particles or grains and describes the behavior of a fictitious granular material along a slope with a wide thickness. The triggering of the landslide is caused by the passing of two conditions: a threshold speed and a condition on the static friction of the particles, the latter based on the Mohr-Coulomb failure criterion according to the infiltration processes. In our scheme the positive pure pressures, that have local value, should be simply interpreted as a perturbation of the rest state of each grain, i.e., the pore pressure function can be interpreted as a time-space dependent scalar field acting on the particles. The resulting numerical method, similar to that of molecular dynamics (MD), is based on the use of an interaction potential between the particles, similar to the Lennard-Jones one. Moreover by means of this type of force we can also simulate a compressed state of the particles, according to a stress state of the slope material. Although the models proposed are still quite schematic, our results encourage the investigations in this direction. The results are consistent with the behavior of real landslides induced by rainfall and an interesting behavior emerges from the dynamical and statistical points of view. Emerging phenomena such as fractures, detachments and arching can be observed (Martelloni et al., 2012; Martelloni et al., 2013). In particular, the models reproduce well the energy and time distribution of avalanches, analogous to the observed Gutenberg-Richter and Omori power law distributions for earthquakes. We observe a power law distribution also considering the number of the particles in motion. We note that other natural hazards (landslides, earthquakes and forest fires) also exhibit similar distributions (Malamud et al., 2004; Turcotte 1997), characteristic of self-organized critical systems (Turcotte and Malamud 2004). From statistical point of view we observe an interesting characteristic of this type of systems, i.e., a transition of the mean energy increment distribution from a Gaussian to a power law after decreasing the viscosity coefficient up to zero. This behavior is compatible with the corresponding velocity increase, i.e., such cross-over in the distribution means that we pass from a relative slow movement to a relative fast slow movement. This results is obtained also within a single simulation for fixed viscosity coefficient (also for zero value of this parameter), i.e., if we consider the distribution of kinetics increment in an initial phase of movement of the system we observe a Gaussian distribution (all particles have similar velocity), while, continuing the simulation, a power law is detected due the presence of particles at higher velocity. Actually, we observe a characteristic velocity and energy pattern typical of a stick-and-slip dynamics, similar to real landslides behavior (Sornette et al., 2004). We have also shown that it is possible to apply the method of the inverse surface displacement velocity for predicting the failure time (Fukuzono 1985). Then we achieve a complete sensibility analysis of the 2D model parameters considering also the fluctuations necessary to take into account the variability of the soil. Moreover the simulations are achieved considering both initial regular configuration of the grains and random configuration ones where each particle is shifted from equilibrium state according to a Gaussian distribution of the position shifts. In conclusion the results of 2D and 3D models are similar, but the three-dimensional scheme allow a better stability concerning the observed kinetics energy and velocity that can become very high for some particles, during the slip, due to the effect of the repulsive forces, obviously equal values of the potential parameters.

References
Fukuzono T (1985) A new method for predicting the failure time of a slope. Proc. 4th Int. Conf. Field Workshop Landslides, 145-150. Tokyo: Jpn. Landslide Soc.
Malamud BD, Turcotte DL, Guzzetti F, Reichenbach P (2004) Landslide inventories and their statistical properties. Earth Surface Processes and Landforms, 29: 687-711
Martelloni G, Bagnoli F, Massaro E (2012) A computational toy model for shallow landslides: Molecular Dynamics approach. Communications in Nonlinear Science and Numerical Simulation
Martelloni G., Bagnoli F. (2013) Infiltration effects on a two-dimensional molecular dynamics model of landslides. In NHAZ (Natural Hazards).
Sornette D, Helmstetter A, Grasso JR, Andersen JV, Gluzman S, Pisarenko V (2004) Towards Landslide Predictions: Two Case Studies. Physica A, 338: 605-632
Turcotte DL (1997) Fractals and chaos in geology and geophysics. Cambridge University Press, Cambridge, (2nd Edition)
Turcotte DL, Malamud BD (2004) Landslides, forest fires, and earth-quakes:examples of self-organized critical behavior. Physica A, 340: 580-589

We illustrate two projects in which we are involved: "La scienza ha fatto rete" (networking Italian science cafes) and "Scicafè2.0". For the first project we present the italian web site of the network. The "SciCafe2.0" project aims at exploiting the knowledge and the "best practices" accumulated during the Science Cafés experience for promoting crowdsourcing and collective intelligence, in an Internet scenario (mixed with real-life encounters) for the Collective Awareness Platforms UE call. In particular, we discuss the cognitive background below a "human" partecipative Internet platform.
Finally, we present some examples of our radio transmission "RadioMoka"

In collaboration with: F. Bagnoli and R. Nerattini.

The random energy landscapes developed by speckle fields can be used to confine and manipulate a large number of micro-particles with a single laser beam. By means of molecular dynamics simulations, we investigate the static and dynamic properties of an active suspension of swimming bacteria embedded into speckle patterns. Looking at the correlation of the density fluctuations and the equilibrium density profiles, we observe a crossover phenomenon when the forces exerted by the speckles are equal to the bacteria's propulsion.

The understanding of the spin-related processes and spin transport in GaAs, Si and related compounds is important for solid state physics and possible applications of these materials in spintronics. Research in the field of spin-electronics are motivated by the possibility to develop electronic devices that use the electron spin rather than charge as a state variable for processing and storing information. This could allow low-power operation and might also have applications in quantum computing. However, the utilization of spin polarization as information carrier must face the disadvantage that each initial non-equilibrium orientation decays over time during the transport. Hence, to open the way to implementation of spin-based devices, the features of spin relaxation at relatively high temperatures, jointly with the influence of transport conditions, should be firstly fully understood and interpreted in experiment-related terms, in order to find out the best conditions to achieve long spin relaxation times (or spin diffusion lengths) in spintronic devices. In this contribution we show the results of numerical calculations of the spin lifetime for conduction electrons drifting in lightly doped n-type GaAs or Silicon channels in the presence of static or fluctuating electric fields. To model both electronic and spin dynamics and to estimate the spin relaxation time, we employ a semiclassical ensemble Monte Carlo method. Our findings are in good agreement with those obtained by using different theoretical approaches and with the most recent experimental results obtained in spin transport devices. Moreover, we also show and discuss how spin lifetimes change in a wide range of temperature and electric field amplitude, even where experimental and/or analytical data are not yet available. From this point of view, the results obtained by our Monte Carlo simulations represent a guide for future experimental studies and could be very useful in a more effective optimization of room-temperature semiconductor- based spintronic devices.

In collaboration with: , N. Pizzolato S. Spezia, C. Graceffa and B. Spagnolo

The classical one-dimensional (1D) planar spin model with competing nearest neighbor (nn) and next nearest neighbor (nnn) exchange interactions (\(Jnn>0\) and \(Jnnn<0\), respectively) was introduced decades ago [1] to account for the observation of a modulated phase (a spiral or helicoid) in a class of magnetic crystals and alloys, including rare-earth elements and manganese compounds. In the thermodynamic limit, the modulated phase was proved to exist provided that \(G=Jnn/(4|Jnnn|)<1\) and the relative angle between neighboring spins is given by \(+arccos(G)\) or \(-arccos(G)\). Opposite signs correspond to equivalent helicoids with opposite sense of rotation (or chirality). In the present work, we investigate the effect of finite size on the equilibrium states of such a model. We are driven by the interest for artificially created nanoscale magnetic structures: for example, an ultrathin film of Ho [2], made of N parallel ferromagnetic planes, where the vector magnetization of each atomic layer is confined to the film plane and is exchange coupled to the magnetization of neighboring layers, with opposite signs of the exchange constant depending on the layers' position (positive between nn layers and negative between nnn ones). Finding the magnetization profile across the film thickness, while accounting for the discrete location of atomic layers, is a difficult task even in a mean field approximation, where the problem is reduced to a 1D one, since it requires the necessity to solve a system of \((N-1)\) equations, for the \((N-1)\) relative orientation angles, obtained after the minimization of the thermodynamic potential. Except for very small values of \(N\), finding the exact solution is quite demanding; thus, to obtain an estimate of the equilibrium configurations, most authors resorted either to time-consuming iterative procedures [2] or to a continuous approximation which allowed to obtain analytical results [3]. In this work we make use of a theoretical method [4], recently developed to find the noncollinear canted magnetic states of ultrathin ferromagnetic films with competing surface and bulk anisotropies [5], to calculate the magnetization profile in the case of our model with competing nn and nnn exchange interactions. The essence of the method is to reduce the difficult problem of finding minima of the thermodynamic potential in the \((N-1)\)-dimensional space of the \((N-1)\) relative orientation angles, to the much simpler problem of finding the \((N-1)\) roots of a function in the one-dimensional space of the first relative orientation angle. Subsequently, the roots are analyzed in order to determine which of them correspond to stable, metastable or unstable states. In this way, we were able to determine, in a very quick and quite accurate way, the equilibrium states of the model up to \(N=15\). In addition to the ground state, which is symmetric with respect to the center of the chain (or, equivalently, to the center of the film), we found metastable states of two kinds: either antisymmetric or without a definite symmetry ("ugly" states). In the ground state, the modulated configuration is non uniform along the finite size of the chain, but the chirality of the helicoid does not change. In contrast, the metastable states are characterized either by a change of chirality in the middle of the chain (antisymmetric state) or a change of chirality located away from the middle of the chain ("ugly" state). The above interpretation was confirmed performing a further analysis of the various modulated configurations in the framework of a discrete nonlinear mapping approach developed years ago [6]. The most interesting result, coming from our exact calculations, is that the antisymmetric states are metastable for even values of \(N\) and unstable for odd values of \(N\), while the "ugly" states are always metastable. This fact, being a consequence of discretization and finite size, can by no means be evidenced using a continuum model [3]. Clearly, as \(N\) grows, any difference between even and odd number of \(N\) is found to decrease, and for \(N\) tending to infinity it is expected to vanish.

[1] T. A. Kaplan, Phys. Rev. 116, 888 (1959); A. Yoshimori, J. Phys. Soc. Jpn. 14, 807 (1959); J. Villain, J. Phys. Chem. Solids 11, 303 (1959).
[2] E. Weschke et al., Phys. Rev. Lett. 93, 157204 (2004).
[3] P. I. Melnichuk, A. N. Bogdanov, U. K. Roessler, and K.-H. Mueller, J. Magn. Magn. Mater. 248, 142 (2002).
[4] A. P. Popov, A. V. Anisimov, O Eriksson, and N. V. Skorodumova, Phys. Rev. B 81, 054440 (2010).
[5] A. P. Popov, J. Magn. Magn. Mater. 324, 2736 (2012).
[6] L. Trallori, P. Politi, A. Rettori, M. G. Pini, and J. Villain, Phys. Rev. Lett. 72, 920 (1994).


In collaboration with A.P. Popov and A. Rettori

Studying the interaction of a quantum system with its environment plays a fundamental role in the development of quantum technologies. De- coherence may be induced by classical or quantum noise, i.e. by the inter- action with an environment described classically or quantum-mechanically. The classical description is often more realistic for environments with a very large number of degrees of freedom and it has also been shown that even certain quantum environments may be described with equivalent classical models. In this work, we consider single- and two-qubit systems coupled to classical stochastic fields, focusing on Gaussian processes, and address both the dynamics of quantum correlations, entanglement and discord, and the non-Markovianity induced by the external fields.

In this work we consider a simple random walk embedded on a two-dimensional regular comb and we address two, intrinsically related problems, i.e. the set of hitting times \(\{ H_{ij} \}\) and the covering time \(\tau\). As for the former, by exploiting the resistance method, we get analytically the exact expression for the set of hitting times, whose mean directly gives the global mean first passage time on combs. We also notice that the mean time to first reach any end-node of a side chain, starting from the backbone, scales as \(\sim L^3\). This turns out to be the leading term for the covering time, as shown via numerical simulations. Finally, we investigate the problem of "imperfect covering", where we look for the mean time \(\tau(x)\) such that a fraction \(x\) of the underlying structure has been covered. The growth of \(\tau(L,x) \approx (a x^{-2/3}-b)\log (L)\) suggests optimization strategies, as a confidence interval of \(1\%\) allows a drastic reduction of the covering time: \(\tau(2^{10},1) / \tau(2^{10},0.99) \approx 3\).

The motility of microorganisms like bacteria and protists in liquid media is an important issue and it is not yet fully understood. Previous theoretical approaches dealing with ''microscopic'' description of the motion have modelled the propelling force exerted by the organism itself as a white noise term in the equation of motion. We will present experimental results for protists of the genus Colpidium, ciliates, which do not agree with the white noise hypothesis. We propose a new stochastic model that is in good agreement with the experimental statistical properties of ciliates' motion, such as velocity distribution, velocity autocorrelation and mean square displacement.