Transport and dynamics in aperiodic systems

Abstract

We aim at investigating various transport and dynamical properties of low-dimensional aperiodic systems. The aperiodicity is generated via the modulation of local parameters following sequences obtained by deterministic inflation rules. Such approach allows one to control the induced geometrical fluctuations, characterized by a wandering exponent \omega, offering a generalization of the methods for producing quasiperiodic systems. The common goal is to gauge the effect of varying the exponent \omega in the context of several quantum and classical systems. Explicitly, we intend to study localization, dynamical phase transitions, and energy and magnetization transport in quantum spin chains, as well as the percolation transition in two-dimensional lattices. Such investigations will help to establish a clearer picture regarding the effects of correlated disorder on the behavior of those systems, which is important both at the fundamental level, exploring necessary conditions for reaching thermal equilibrium, but also at the level of potential applications taking advantage of localized states, as in memory storage for quantum computation. (AU)