# Mathematical Challenges of Quantum Transport in Nano-Optoelectronic Systems - Abstract

Racec, Roxana

Fano effect in open quantum systems

We analyze a quantum dot strongly coupled to the conducting leads via quantum point contacts - Fano regime of transport - and report a variety of resonant states which demonstrate the dominance of the interacting resonances in the scattering process in a low confining potential. As effects of the interaction between resonances, the line shapes of the conductance peaks are described by Fano functions with complex asymmetry parameters and the phases of the transmission amplitudes do not increase monotonically by $\pi$ through each conductance peak anymore. The phase lapses, typical for the universal behaviour, are obtained as a particular case for weak interacting resonances, while the strong interaction regime is associated with the mesoscopic phase evolution.