How dynamic quantum system forgets? ——Thermalization in quantum system.

The phenomenon of thermalization, which refers to the process of a dynamic quantum system evolving to thermal equilibrium states, is a ubiquitous occurrence in quantum many-body systems. In such equilibrium states, the system can be described by only a few parameters, which is significantly fewer than the number of degrees of freedom characterizing the system's microscopic state. As a result, during thermalization, the system loses information regarding its initial state. 

This presentation comprises three parts. The first part introduces thermal equilibrium states and thermalization in quantum systems, along with the role of eigenstate thermalization hypothesis(ETH) in ensuring thermalization. The second part provides counterexamples to thermalization in certain systems, including integrable system, many-body localization, quantum many-body scar and measurement induced phase transition. Finally, the third part examines prethermalization, a phenomenon that arises when there is a clear distinction between relevant time scales and has various physical origins depending on the system in question. In prethermalization, the system may take an exponentially long time to thermalize.

Mori, Takashi, et al. "Thermalization and prethermalization in isolated quantum systems: a theoretical overview." Journal of Physics B: Atomic, Molecular and Optical Physics 51.11 (2018): 112001.