Title: "Topological invariants and perturbation theory in disordered and mesoscopic systems using the kernel polynomial method"

Abstract: "We present new algorithms based on the kernel polynomial method, that allow us to study the topology and response of samples with more than 10^7 degrees of freedom. We calculate topological invariants of bulk disordered insulators, such as alloys, quasicrystals, and amorphous systems. In particular, we apply our method to the mirror Chern number using an atomistic model of PbSnTe alloy and tighten the critical concentration for the phase transition. We also develop the hybrid kernel polynomial method, which allows accurate and efficient treatment of both subgap and continuum states. We use this approach to improve the computation of supercurrent and inductance in a Josephson junction, and the construction of perturbative effective Hamiltonians describing the interaction of spin qubits defined in a two dimensional electron gas."