The MSc student shall study dynamical correlations and tunneling spectra in the infinite temperature Hubbard model using perturbation theory. Since the Matsubara method is not applicable, a Keldysh approach shall be employed, and the self-energy and spectral functions shall be determined using diagrammatic perturbation theory. Results shall be compared with Matrix-Product-State (MPS) simulations. As an extension, a third quantization approach shall be used to reproduce the results, and include dissipative effects such as the presence of sinks.