Atypicality of thermalization in disordered many-body quantum systems

Thermalization in generic isolated many-body quantum systems is well understood in the successful framework of the eigenstate thermalization hypothesis (ETH). Since the last decade, strongly disordered systems have been a candidate to evade thermalization and show many-body localization (MBL). In this talk, I will discuss the fate of thermalization for a disordered chain in contact with a clean chain by probing the spin transport between the two. Surprisingly, for a wide range of disorder strengths, the transport is highly atypical across different realizations, encoding strong sample-to-sample fluctuations. In addition to this, for a disordered chain of fixed length, the threshold disorder strength after which inhibition of transport becomes typical shows a concomitant growth with the length of the clean chain. To understand such behavior analytically, I will discuss a perturbative scheme along with extreme value theory.