A quantization theorem for the edge currents is proven for discrete magnetic half-plane
operators. Hence the edge channel number is a valid concept also in presence of a …

Topological insulators are crystalline solids with supposedly very special properties. If
stumbling upon such a crystal, which is possible because topological insulators are known …

This book provides an introduction to the mathematical theory of disorder effects on quantum
spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics …

These lecture notes review the theory of transport in aperiodic solids based on
noncommutative geometry. Revisiting transport theory is motivated by the large variety of …

Quantum transport is investigated by a suitable development of the Kubo formula on a basis
of orthogonal polynomials and by using real-space recursion principle. The general method …

A random polymer model is a one-dimensional Jacobi matrix randomly composed of two
finite building blocks. If the two associated transfer matrices commute, the corresponding …

The search for strong topological phases in generic aperiodic materials and meta-materials
is now vigorously pursued by the condensed matter physics community. In this work, we first …

A concrete strategy is presented for generating strong topological insulators in d+ d′
dimensions which have quantized physics in d dimensions. Here, d counts the physical and …

We justify the linear response theory for an ergodic Schrödinger operator with magnetic field
within the noninteracting particle approximation, and derive a Kubo formula for the electric …

We derive a generalized Drude formula for the optical conductivity of quasicrystals,
assuming a diffusion law in a perfect quasicrystal L (t)∝ t β, where L (t) measures the …