The physics of disordered quantum systems – Bigger, smaller and alive
Abstract
In this talk, I will review recent advances in the theoretical and computational approaches to some condensed-matter systems.
My first example will be a short introduction to the fascinating physics of disorder quantum systems exhibiting the disorder-induced phenomenon of Anderson localization. In three spatial dimensions, these systems can be driven from a metal to an insulator by changing their disorder-content. Experimentally, this can be done by changing the dopant concentration, the temperature or an external pressure. Close to the transition, these systems show scaling and the electronic states seem to be multifractals, i.e., entities which are fractals of fractals. The study of such states relies on being able to diagonalize the corresponding Schrödinger equation for very large systems. I will show results where we have been able to diagonalize
the Hamiltonian matrix with up to 4003 x 4003 = 64,000,000 x 64,000,000 matrix entries.
The driving principle in the above transition is the electronic self-interference by backscattering at the impurity sites, leading to regions where the electronic wave function interferes constructively- the localization centres - or deconstructively. Similarly, we can study effects of self-interference when using topological constraints. As an example, I will study the interacting motion of an optically excited electron and hole pair a so-called exciton on a ring which is only a few times larger than the excitonic Bohr radius. In this case, it turns out that the exciton interferes with itself and this in turn leads to oscillations in the excitonic spectra. These have recently been found experimentally.
As a last example, I consider the possibility of electronic transport along segments of DNA. Here, both the experimental and the theoretical situation is far from clear, apparently contradictory experiments and a host of attempts at modelling charge transport in DNA exist. I will review the current situation and show how the quantum motion of electronic charge again leads to initially unexpected behaviour such a delocalization due to disorder.
