Levy ratchets with dichotomic random flashing

Additive symmetric Levy noise can induce directed transport of overdamped particles in a static asymmetric potential. We study, numerically and analytically, the effect of an additional dichotomous random flashing in such Levy ratchet system. For this purpose we analyze and solve the corresponding fractional Fokker-Planck equations and we check the results with Langevin simulations. We study the behavior of the current as function of the stability index of the Levy noise, the noise intensity and the flashing parameters. We find that flashing allows both to enhance and diminish in a broad range the static Levy ratchet current, depending on the frequencies and asymmetry of the multiplicative dichotomous noise, and on the additive Levy noise parameters. Our results thus extend those for dichotomous flashing ratchets with Gaussian noise to the case of broadly distributed noises.

Ground-state topology of the Edwards-Anderson +/-J spin glass model

In the Edwards-Anderson model of spin glasses with a bimodal distribution of bonds, the degeneracy of the ground state allows one to define a structure called backbone, which can be characterized by the rigid lattice (RL), consisting of the bonds that retain their frustration (or lack of it) in all ground states. In this work we have performed a detailed numerical study of the properties of the RL, both in two-dimensional (2D) and three-dimensional (3D) lattices. Whereas in 3D we find strong evidence for percolation in the thermodynamic limit, in 2D our results indicate that the most probable scenario is that the RL does not percolate. On the other hand, both in 2D and 3D we find that frustration is very unevenly distributed. Frustration is much lower in the RL than in its complement. Using equilibrium simulations we observe that this property can be found even above the critical temperature. This leads us to propose that the RL should share many properties of ferromagnetic models, an idea that recently has also been proposed in other contexts. We also suggest a preliminary generalization of the definition of backbone for systems with continuous distributions of bonds, and we argue that the study of this structure could be useful for a better understanding of the low temperature phase of those frustrated models.