Transição entre os comportamentos estendido e localizado em caminhadas estocásticas parcialmente auto-repulsivas em sistemas desordenados unidimensionais / Transition between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systems

AUTOR(ES)

Juliana Militão da Silva Berbert

DATA DE PUBLICAÇÃO

2009

RESUMO

Consider $N$ sites randomly and uniformly distributed in a $d$-dimensional hypercube. A walker explores this disordered medium going to the nearest site, which has not been visited in the last $\mu$ (memory) steps. The walker trajectory is composed of a transient part and a periodic part (cycles). In this case, travelers can or cannot explore all available space, given rise to a crossover at critical memory, for one-dimensional systems $\mu_1=\log_2{N}$, between localized and extended regimes. % as function of $\mu$. The deterministic rule can be softened to consider more realistic situations with the inclusion of a stochastic parameter $T$ (temperature). In this case, the walker movement is defined by a probability density function (PDF) that is parameterized by $T$ and a cost function, which increases as the distance among sites increases. The PDF is chosen to favor hops to nearest sites. As the temperature increases, the walker can escape from cycles and extend the exploration. Here we report the analytical and numerical studies of the influence of the temperature and the critical memory in the exploration of a one-dimensional disordered system.

ASSUNTO(S)

aging caminhadas estocásticas deterministic walk envelhecimento glass transition complex systems stochastic walk caminhadas deterministas optimization problems. sítios acessíveis sistemas complexos transição vítrea problemas de otimização. accessible sites sistemas fora do equilíbrio disordered systems sistemas desordenados systems out-of-equilibrium

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