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This course explores ergodicity breaking in quantum many-body systems, focusing on two mechanisms: many-body localisation and the competition between quantum dynamics and measurements. The learning outcomes include understanding the conditions for non-ergodic behavior, the nature of phase transitions, and the dynamics of quantum entanglement. The course teaches theoretical approaches from the perspective of many-body Hilbert/Fock spaces and includes topics such as thermalization, quantum phase transitions, and numerical studies. The teaching method involves lectures and discussions. This course is intended for individuals interested in quantum mechanics, statistical mechanics, and theoretical physics.
