I will present a study of integrable structures and quantum chaos in a class of infinite-dimensional though computationally tractable models, called quantum resonant systems. These models, together with their classical counterparts, emerge in various areas of physics, such as nonlinear dynamics in anti-de Sitter spacetime, but also in Bose-Einstein condensate physics. The class of classical models displays a wide range of integrable properties, such as the existence of Lax pairs, partial solvability or generic chaotic dynamics. This opens a window to investigate these properties from the perspective of the corresponding quantum theory by effectively diagonalising finite-sized matrices and exploring level spacing statistics. We will furthermore analyse the implications of the symmetries for the spectrum of resonant models with partial solvability and discuss how the rich integrable structures can be exploited to constructed novel quantum coherent states that effectively capture sophisticated nonlinear solutions in the classical theory.
