Abstract:
In this work we study the transport properties of non-interacting overdamped particles, moving on tilted disordered potentials, subjected to Gaussian white noise. We give exact formulas for the drift and diffusion coefficients for the case of random potentials resulting from the interaction of a particle with a "random polymer". In our model the "random polymer" is made up, by means of some stochastic process, of monomers that can be taken from a finite or countable infinite set of possible monomer types. For the case of uncorrelated random polymers we found that the diffusion coefficient exhibits a non-monotonous behavior as a function of the noise intensity. Particularly interesting is the fact that the relative diffusivity becomes optimal at a finite temperature, a behavior which is reminiscent to that of stochastic resonance. We explain this effect as an interplay between the deterministic and noisy dynamics of the system. We also show that this behavior of the diffusion coefficient at a finite temperature is more pronounced for the case of weakly disordered potentials. We test our findings by means of numerical simulations of the corresponding Langevin dynamics of an ensemble of noninteracting overdamped particles diffusing on uncorrelated random potentials.

Abstract:
In this work we study the diffusion of non-interacting overdamped particles, moving on unbiased disordered correlated potentials, subjected to Gaussian white noise. We obtain an exact expression for the diffusion coefficient which allows us to prove that the unbiased diffusion of overdamped particles on a random polymer does not depend on the correlations of the disordered potentials. This universal behavior of the unbiased diffusivity is a direct consequence of the validity of the Einstein relation and the decay of correlations of the random polymer. We test the independence on correlations of the diffusion coefficient for correlated polymers produced by two different stochastic processes, a one-step Markov chain and the expansion-modification system. Within the accuracy of our simulations, we found that the numerically obtained diffusion coefficient for these systems agree with the analytically calculated ones, confirming our predictions.

Abstract:
We study one-dimensional lattice systems with pair-wise interactions of in?nite range. We show projective convergence of Markov measures to the unique equilibrium state. For this purpose we impose a slightly stronger condition than summability of variations on the regularity of the interaction. With our condition we are able to explicitly obtain stretched exponential bounds for the rate of mixing of the equilibrium state. Finally we show convergence for the entropy of the Markov measures to that of the equilibrium state via the convergence of their topological pressure.

Abstract:
In this work we study the transition from normal to anomalous diffusion of Brownian particles on disordered potentials. The potential model consists of a series of "potential hills" (defined on unit cell of constant length) whose heights are chosen randomly from a given distribution. We calculate the exact expression for the diffusion coefficient in the case of uncorrelated potentials for arbitrary distributions. We particularly show that when the potential heights have a Gaussian distribution (with zero mean and a finite variance) the diffusion of the particles is always normal. In contrast when the distribution of the potential heights are exponentially distributed we show that the diffusion coefficient vanishes when system is placed below a critical temperature. We calculate analytically the diffusion exponent for the anomalous (subdiffusive) phase by using the so-called "random trap model". We test our predictions by means of Langevin simulations obtaining good agreement within the accuracy of our numerical calculations.

Abstract:
The time-dependent probability density function of a system evolving towards a stationary state exhibits an oscillatory behavior if the eigenvalues of the corresponding evolution operator are complex. The frequencies \omega_n, with which the system reaches its stationary state, correspond to the imaginary part of such eigenvalues. If the system is further driven by a small and oscillating perturbation with a given frequency \omega, we formally prove that the linear response to the probability density function is enhanced when \omega = \omega_n. We prove that the occurrence of this phenomenon is characteristic of systems that reach a non-equilibrium stationary state. In particular we obtain an explicit formula for the frequency-dependent mobility in terms of the of the relaxation to the stationary state of the (unperturbed) probability current. We test all these predictions by means of numerical simulations considering an ensemble of non-interacting overdamped particles on a tilted periodic potential.

Abstract:
We study the diffusion of an ensemble of overdamped particles sliding over a tilted random poten- tial (produced by the interaction of a particle with a random polymer) with long-range correlations. We found that the diffusion properties of such a system are closely related to the correlation function of the corresponding potential. We model the substrate as a symbolic trajectory of a shift space which enables us to obtain a general formula for the diffusion coefficient when normal diffusion occurs. The total time that the particle takes to travel through n monomers can be seen as an ergodic sum to which we can apply the central limit theorem. The latter can be implemented if the correlations decay fast enough in order for the central limit theorem to be valid. On the other hand, we presume that when the central limit theorem breaks down the system give rise to anomalous diffusion. We give two examples exhibiting a transition from normal to anomalous diffusion due to this mechanism. We also give analytical expressions for the diffusion exponents in both cases by assuming convergence to a stable law. Finally we test our predictions by means of numerical simulations.

Abstract:
In this note we study a class of one-dimensional Ising chain having a highly degenerated set of ground-state configurations. The model consists of spin chain having infinite-range pair interactions with a given structure. We show that the set of ground-state configurations of such a model can be fully characterized by means of symbolic dynamics. Particularly we found that the set ground- state configurations defines what in symbolic dynamics is called sofic shift space. Finally we prove that this system has a non-vanishing residual entropy (the topological entropy of the shift space), which can be exactly calculated.

Abstract:
We introduce a method to estimate the complexity function of symbolic dynamical systems from a finite sequence of symbols. We test such complexity estimator on several symbolic dynamical systems whose complexity functions are known exactly. We use this technique to estimate the complexity function for genomes of several organisms under the assumption that a genome is a sequence produced by a (unknown) dynamical system. We show that the genome of several organisms share the property that their complexity functions behaves exponentially for words of small length $\ell$ ($0\leq \ell \leq 10$) and linearly for word lengths in the range $11 \leq \ell \leq 50$. It is also found that the species which are phylogenetically close each other have similar complexity functions calculated from a sample of their corresponding coding regions.

Abstract:
Apesar das pesquisas com sistemas silvipastoris terem sido iniciadas no final da década de 1970, as informa es geradas até hoje n o s o em grande número. As vantagens advindas de um sistema silvipastoril s o inúmeras e devidamente reconhecidas. Pelo fato de ser uma técnica de uso da terra capaz de recuperar ecossistemas alterados pelo mau manejo, estes sistemas, pela integra o de atividades agrícolas, pecuárias e silviculturais, passam a representar uma tecnologia que confere maior sustentabilidade que os sistemas tradicionais, nos quais os monocultivos s o predominantes. Nos últimos anos, institui es de ensino, pesquisa e extens o do País têm se voltado para o desenvolvimento de tais sistemas. O governo de Minas Gerais, por meio de sua Secretaria de Estado de Agricultura e de órg os vinculados, vem promovendo a condu o de modelos agrossilvipastoris num processo integrado de ocupa o do solo, denominado lavoura-pecuária-silvicultura. Apesar dos grandes avan os no conhecimento de culturas anuais e dos componentes arbóreos, principalmente o eucalipto, e de gramíneas forrageiras tolerantes à diminui o da intensidade luminosa, ainda é necessário se comnhecer melhor o manejo do sub-bosque sob os efeitos do pastejo. doi: 10.4336/2009.pfb.60.77 Although researches related to silvopastoral systems have been initiated many years ago in Brazil, there are few informations generated until now. The advantages from a silvopastoral system are inumerous and well recognized. By the fact of being a technique of land using capable of recovering several disturbed ecosystems, the silvopastoral systems by the integration of agricultural, cattle, and silvicultural activities represent a technology that can achieve higher sustainability than the traditional systems as the monocultures. Today, research centers in Brazil dedicate great attention to agrossilvopastoral systems. The government of Minas Gerais State, through the extension offices is promoting the agricultural, cattle and silvicultural practices in an integrated process of soil occupation. Even with good level of knowledge about annual crops, trees components, an example eucalyptus, and forage grasses tolerant to lower light intensity, it is necessary a better knowledge of the management of understory under the effects of grazing.

Abstract:
A continuous-variable quantum key distribution protocol based on squeezed states and heterodyne detection is introduced and shown to attain higher secret key rates over a noisy line than any other one-way Gaussian protocol. This increased resistance to channel noise can be understood as resulting from purposely adding noise to the signal that is converted into the secret key. This notion of noise-enhanced tolerance to noise also provides a better physical insight into the poorly understood discrepancies between the previously defined families of Gaussian protocols.