We give a comprehensive presentation of a renormalization-group theory for the study of a
set of one-dimensional Schrödinger equations on quasicrystalline and hierarchical …

Localization lengths of electronic states on one-dimensional Fibonacci quasicrystals are
calculated exactly within a decimation-renormalization scheme. A self-similar pattern is …

The electronic spectrum of the Penrose rhombus quasicrystal exhibits a macroscopic
fraction of exactly degenerate zero-energy states. In contrast to other bipartite quasicrystals …

We study the superconducting proximity effect in inhomogeneous systems in which a
disordered or quasicrystalline normal-state wire is connected to a BCS superconductor. We …

Structural defects are inherent in solids at a finite temperature, because they diminish free
energies by growing entropy. The arrangement of these defects may display long-range …

The unavoidable coupling of quantum systems to external degrees of freedom leads to
dissipative (nonunitary) dynamics, which can be radically different from closed-system …

We re-examine the conventional idea of determining the nature of the electronic
eigenfunctions (extended, critical or localised) of a Fibonacci lattice from a study of the …

An exact real-space renormalization-group approach is developed to calculate the local
Green's function and the local density of states at any site in an infinite Fibonacci chain, in …

A real-space renormalization group (RSRG) scheme is developed to calculate the local
Green's functions for electrons in two-dimensional quasi-crystals. The RSRG transformations …

The energy spectra of quasi-one-dimensional quasiperiodic ladder networks are analyzed
within a tight binding description. In particular, we show that if a selected set of sites in each …