Non Hermitian dynamics of disordered media and interacting atomic Bose-Einstein Condensates

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The propagation of waves through complex media is an interdisciplinary problem that addresses areas as diverse as electronic and atomic-matter waves, to light propagation used to transmit energy and information. Despite this diversity, the wave character of these systems provides a common framework for understanding their transport properties and often leads to new applications. In this project, we focus our research efforts in understanding wave propagation in disordered media while at the same time we investigate how non-linearities due to Kerr effect or due to atom-atom interactions affect the transport. Specifically, we address the following questions : (a) branching of electron flow in semiconductor nanostructures due to scattering from smoothly correlated disorder; (b) propagation of photons in coupled waveguides with anti-linear symmetries; (c) non-hermitian dynamics of atomic BECs in optical lattices with gain/loss; (d) chaotic scattering from a BEC loaded in small optical lattices and (e) Aharonov-Bohm oscillations in disordered non-linear ring geometries.