Conveners
Tutorial Lecture: Relaxation and its breakdown in open quantum systems: Tutorial Lecture
- Ryusuke Hamazaki (RIKEN)
Description
Recent developments of quantum simulators and quantum computers have enabled us to realize and engineer quantum many-body dynamics in a highly controllable manner. This has motivated researchers to revisit the foundations of statistical mechanics from quantum mechanics, a subject that dates back to von Neumann's seminal work about a century ago. In this tutorial talk, I will give an introductory review of non-equilibrium dynamics in quantum many-body systems.
In the first part, I will review thermalization and its breakdown in closed quantum systems [1,2]. After reviewing how thermalization of pure states is justified by the eigenstate thermalization hypothesis (ETH), I will discuss the relationship between ETH, nonintegrability, and symmetry. I will then overview more exotic mechanisms for the breakdown of thermalization, such as many-body localization, quantum many-body scars, and Hilbert-space fragmentation. Finally, I will review how the second law of thermodynamics in closed systems, which cannot be understood solely in terms of thermalization, can be justified in quantum many-body systems.
In the second part, I will consider relaxation and its breakdown in open quantum systems, including systems subject to quantum measurement [3]. I will first explain the basics of measurement theory and the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. Then, steady-state structures and relaxation toward them will be discussed from the viewpoint of Liouvillian spectra and strong symmetries. Finally, I will discuss measurement-induced transitions of quantum trajectories from the viewpoint of purification and the Lyapunov spectrum.
[1] L. D’Alessio et al., Advances in Physics 65.3 (2016).
[2] S. Moudgalya et al., Rep. Prog. Phys. 85 086501 (2022).
[3] RH, K Mochizuki, H Oshima, and Y Fuji, PTEP, ptag055 (2026).