Effective field theories for disordered systems from the logarithmic derivative of the wave-function

[摘要] ENGLISH ABSTRACT:In this dissertation, we give an overview of disordered systems, where we concentrate on thetheoretical calculation techniques used in this field. We first discuss the general properties ofdisordered systems and the different models and quantities used in the study of these systems,before describing calculation techniques used to investigate the quantities introduced. Thesecalculation techniques include the phase formalism method used one dimension, as well as thescaling approach and field theoretic approaches leading to non-linear c-models in higher dimensions.We then introduce a complementary effective field theoretic approach based on thelogarithmic derivative of the wave-function, and show how the quantities of interest are calculatedusing this method. As an example, the effective field theory is applied to one dimensionalsystems with Gaussian disorder. The average density of states, the average 2-point correlatorand the conductivity are calculated in a weak disorder saddle-point approximation and in strongdisorder duality approximation. These results are then calculated numerically and in the case ofthe density of states compared to the exact result.

[发布机构] Stellenbosch University