Various properties of underdoped superconducting cuprates, including the momentum-dependent pseudogap opening, indicate a behavior which is neither BCS nor Bose-Einstein condensation (BEC) like. To explain this issue we introduce a two-gap model. This model assumes an anisotropic pairing interaction among two kinds of fermions with small and large Fermi velocities representing the quasiparticles near the M and the nodal points of the Fermi surface respectively. We find that a gap forms near the M points resulting into incoherent pairing due to strong fluctuations. Instead the pairing near the nodal points sets in with phase coherence at lower temperature. By tuning the momentum-dependent interaction, the model allows for a continuous evolution from a pure BCS pairing (in the overdoped and optimally doped regime) to a mixed boson-fermion picture (in the strongly underdoped regime). PACS numbers:74.20. De, 74.20.Mn, The underdoped cuprates are characterized by a pseudogap opening below a strong doping (δ) dependent crossover temperature T * (δ), above the superconducting critical temperature T c (δ) [1]. By decreasing the doping the temperature T * increases, while the superconducting critical temperature T c decreases until the insulating state is reached. The different behavior of T * and T c as doping is varied, finds a counterpart in the different behavior of the coherence energy scale, obtained in Andreev reflection measurements [2], and the single-particle gap, observed both in angle-resolved photoemission (ARPES) and in tunneling experiments [1]. This has triggered a very active debate on the relevance of a non-BCS superconductivity and of a BCS-BEC crossover in these materials [3][4][5][6]. In particular ARPES shows that below T * the gap opens around the M points of the Brillouin zone [i.e. (±π, 0), (0, ±π)] suggesting that T * can be interpreted as a mean-field-like temperature where electrons start to form local pairs without phase coherence. However, it is also found [7] that below T * substantial portions of the Fermi surface remain gapless. This behavior can be described neither by BCS nor by Bose-Einstein condensation (BEC) schemes. Instead it is suggestive of strong pairing between the states around the M points and of weak coupling near the zone diagonals. Various other experiments [8,9] carried below T c show a doping and temperature dependence of the gap anisotropy and therefore are again suggestive of a strong anisotropy in the pairing potential.In this letter we explore a new direction (neither BCS nor BEC) focusing on the consequences of a strongly anisotropic interaction. To this aim we introduce a twogap model, where strongly paired fermionic states can coexist and interplay with weakly coupled pairs in different regions of the Fermi surface (FS). This line of thinking was partly explored in Refs. [5,6], where only the extreme strong-coupling limit of one component was considered. In particular the view of Ref.[6] would allow to describe only the very underdoped region of the cuprate phase ...

[1] Landslide inventories show that the statistical distribution of the area of recorded events is well described by a power law over a range of decades. To understand these distributions, we consider a cellular automaton model based on a dissipative dynamical variable associated to a time and position dependent factor of safety. The model is able to reproduce the complex structure of landslide distribution, as experimentally reported. In particular, we investigate the role of the rate of change of the system dynamical variables, induced by an external drive, on landslide modeling and its implications on hazard assessment. As the rate is increased, the model has a crossover from a critical regime with power-laws to non power-law behaviors. We suggest that the detection of patterns of correlated domains in monitored regions can be crucial to identify the response of the system to perturbations, i.e., for hazard assessment. Citation: Piegari, E., V. Cataudella, R. Di Maio, L. Milano, and M. Nicodemi (2006), A cellular automaton for the factor of safety field in landslides modeling, Geophys. Res. Lett., 33, L01403,

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We study the superconducting properties of a two-dimensional superconductor in the proximity to an electronic topological transition (ETT). In contrast to the 3D case, we find that the superconducting gap at T = 0, the critical temperature Tc, and the impurity scattering rate are characterized by a nonmonotonic behavior, with maxima occurring close to the ETT. We derive analytical expressions for the value of such maxima both in the s-wave and in the d-wave case. Such expressions are in good qualitative agreement with the phenomenological trend recently observed for T max c as a function of the hopping ratio t ′ /t across several cuprate compounds. We further analyze the effect of an ETT on the Ginzburg-Landau stiffness η. Instead of vanishing at the ETT, as could be expected, thus giving rise to an increase of the fluctuation effects, in the case of momentum-independent electron-electron interaction, we find η = 0, as a result of an integration over the whole Fermi surface.