Abstract

The long time dynamics of disordered quantum many-body systems close to a many-body localisation (MBL) regime is strongly influenced by various types of rare events: Rare regions of low disorder drive the genuine delocalisation transition in 1d lattice systems, and are believed to destroy the MBL phase in higher dimensions. Rare fluctuations of energy or density control the bad conductivity in the barely delocalised phase, while rare regions of strong disorder were argued to induce a phase with subdiffusive transport in a finite parameter window from the localisation transition in 1d system. I will review these different types of rare events and discuss how they fit together in a bigger picture of MBL and quasi MBL systems.