MSc defense by Mads Rud Larsen
Random matrix theory of Majorana nanowires
A two-flavour random matrix model is investigated, motivated by the studies of topological superconductors in condensed matter physics and the work on topological zero modes. Specifically, a robust \tau_2-chirality of the Majorana zero modes is introduced. The eigenvector statistics of the \tau_2-chirality including perturbations are presented numerically, and are proposed to be calculated from a partially quenched supersymmetric partition function.
This thesis provides the foundations to be able to find an analytic expression of the eigenvector statistics. In doing this, we reproduce an exact expression of the spectral density of antisymmetric matrices of finite matrix dimension, as well as we reproduce the spectral density in the limit of infinite dimensions. In addition to this, we calculate the two-flavour fermionic partition function including a general and a special case perturbation. These calculations demonstrate the ability of explicitly deriving the effective field theory (EFT) from random matrix theory (RMT).