Sommerfeld Theory Colloquium, Do quantum many-body systems necessarily come to thermal equilibrium

after a long enough time evolution? The conventional wisdom

has long been that they do and that, in the process, any quantum

information encoded in the initial state is lost irretrievably. Thus the

dynamics of many-interacting particles becomes effectively classical.

But these ingrained notions of thermalization and ergodicity have

recently been called into question. In this talk I will discuss how

ergodicity can break down in disordered quantum systems through

the phenomenon of many-body localization. In contrast to thermalizing

fluids, quantum correlations can persist through time evolution

of the localized state even at high energy densities. Thus, investigating

the many-body localization transition offers a concrete route

to address fundamental unsolved questions concerning the boundary

between classical and quantum physics in the macroscopic world. I

will emphasize the important role that quantum entanglement plays

in current attempts to understand this fascinating dynamical phase

transition. Finally I will present recent progress in confronting the

emerging theoretical understanding of many-body localization with

experimental tests using systems of ultra-cold atoms.