Statistics of wave functions in coupled chaotic systems

Using the supersymmetry technique, we calculate the joint distribution of local densities of electron wave functions in two coupled disordered or chaotic quantum billiards. We find spatial correlations that are absent in a single chaotic system. Our exact result can be interpreted for small coupling in terms of the hybridization of eigenstates of the isolated billiards. We show that the presented picture is universal, independent of microscopic details of the coupling.

Localization-delocalization transition in non-hermitian disordered systems

Using the supersymmetry technique, we study the localization-delocalization transition in quasi-one-dimensional non-Hermitian systems with a direction. In contrast to chains, our model captures the diffusive character of carriers' motion at short distances. We calculate the joint probability of complex eigenvalues and some other correlation functions. We find that the transition is abrupt and it is due to an interplay between two saddle points in the free energy functional.

Antilocalization in a 2D electron gas in a random magnetic field

We construct a supersymmetric field theory for the problem of a two-dimensional electron gas in a random, static magnetic field. We find a new term in the free energy in addition to those present in the conventional unitary sigma model, whose presence relies on the long-range nature of the disorder correlations. Under a perturbative renormalization group analysis of the free energy, the new term contributes to the scaling function at one-loop order and leads to antilocalization.