The eigenstate thermalisation hypothesis and the quantum many-body scars

The eigenstate thermalisation hypothesis (ETH) represents the current most developed framework to explain the onset of thermalisation in isolated many-body quantum systems. In this thesis we will focus on quantum many-body scars, and in particular on their asymptotic version. Quantum many-body scars are notoriously associated to a non-ergodic dynamics and to relaxation times that diverge in the thermodynamic limit; briefly, these states fail to thermalise. The goal of this thesis is to investigate the violation of ETH associated to asymptotic quantum many-body scars.