| This thesis describes state of the art calculations of transport properties of quantum systems in quasiperiodic, random or deterministically aperiodic potentials. The topics discussed here are not only in the forefront of condensed matter physics but are also one of the grand challenges in computational physics research. Initial research involving non-interacting fermions in aperiodic fields showed that the metal-insulator transition and the existence of an intermediate phase with multifractal wave functions and spectra, known as critical phase, are generic features of these types of systems. Motivated by these results, I studied many-body strongly correlated fermion systems in aperiodic potentials. Using numerical Lanczos diagonalization, the ground state energy and the transport properties of the systems were calculated. The results provide evidence for the existence of a phase that is neither conducting nor insulating. This conjectured new phase may be characterized by a power law scaling with the size of the system. |
