Exact solutions of many-body quantum chaotic systemsKos, Pavel (Avtor) Prosen, Tomaž (Mentor) quantum chaosquantum many-body systemsexact solutionsnon-equilibrium statistical mechanicsFloquet systemsquantum circuitsspectral form factorkicked Ising spin chainsChaotic quantum many-body systems exhibit complex dynamics, which presents an obstacle in their analytical and numerical understanding. Therefore, many aspects of these generic many-body systems are still poorly understood. In this thesis, we present exact solutions for chaotic many-body quantum systems. We focus on kicked Ising spin chains and quantum circuits with an additional property -- dual-unitarity. This property asserts that quantum evolution remains unitary upon switching space and time and it is essential for obtaining exact solutions. We start by focusing on quantum chaos. One of the key goals of quantum chaos is to explain why spectral fluctuations of simple local models match the spectral fluctuations of random matrices. This was resolved in a few-body context using a semiclassical limit but remained enigmatic in many-body contexts without classical limits. After defining the setting, we prove that the spectral fluctuations match random matrix theory in three different cases by computing the Fourier transform of spectral density's two-point function: spectral form factor. This property validates these models as chaotic. Next, we compute the correlation functions in dual-unitary systems and classify them according to different degrees of ergodicity. We further characterise these chaotic systems by examining their dynamical complexity, captured by the local operator entanglement entropy. We proceed beyond previous discussions by treating correlation functions in perturbed dual-unitary models, thus establishing the stability of these models. The quest to obtain rigorous results leads us to a minimal setting of the operator evolution, relevant for noisy (time-depended) systems. In this setting, we can calculate the correlation functions for perturbed dual-unitary models as well as for a new class of chaotic models corresponding to diagrams with no merges. Finally, we use these models to probe the spectral fluctuations in noisy systems, by which we connect the generalised spectral form factor with the correlation functions.20212021-06-20 08:15:02Doktorsko delo/naloga127701sl