We present model calculations of two very different nonlinear phenomena in quantum dot systems. Essential to the description of both aspects is the interplay of the geometry of the system and the numerical exact diagonalization of the system Hamiltonian in a large truncated many-body Fock space. First, we consider the excitation of a collective radial mode in a single quantum dot beyond the linear response. Here, the dynamical Coulomb interaction of the electrons is essential and a simple DFT model fails. Second, we consider the transport of electrons through a system of parallel double quantum dots in a photon cavity. We show that both the para- and the dia-magnetic electron-photon interactions cause a Rabi-resonance in the system that influences the current through it [2,3]. We speculate on the nonlinear character of the diamagnetic interaction.

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[1] Excitation of radial collective modes in a quantum dot: Beyond linear response, Vidar Gudmundsson, Sigtryggur Hauksson, Arni Johnsen, Gilbert Reinisch, Andrei Manolescu, Christophe Besse, and Guillaume Dujardin, Annalen der Physik 526, 235 (2014)

[2] Coupled collective and Rabi oscillations triggered by electron transport through a photon cavity, Vidar Gudmundsson, Anna Sitek, Pei-yi Lin, Nzar Rauf Abdullah, Chi-Shung Tang, and Andrei Manolescu, ACS Photonics 2, 930 (2015)

[3] Electroluminescence caused by the transport of interacting electrons through parallel quantum dots in a photon cavity, Vidar Gudmundsson, Nzar Rauf Abdullah, Anna Sitek, Hsi-Sheng Goan, Chi-Shung Tang, and Andrei Manolescu, Annalen der Physik 530, 1700334 (2018)