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Quantum electronic systems are important for technological innovation and scientific progress. Exploring entanglement and strong correlation in quantum systems can also lead to novel materials and contribute to quantum computing. The focus of this thesis is on quantum electronic systems that lack translational symmetry, where we investigate strong correlation effects due to incommensurate potential, non-linear optical response in disordered systems, and the dynamics of an integrable time-dependent superconductivity model with all-to-all interaction.