Common knowledge tells that many-body systems come to thermodynamic equilibrium by coupling to a heat reservoir. In classical physics, even ideally isolated, macroscopic systems thermalize due to the equivalence of the microcanonical and the canonical ensembles.
However, in quantum dynamics it is a fundamental problem how an isolated quantum many-body system can eventually come to rest from an initial nonequilibrium state, and whether the final state is a thermal one. The problem arises because the time evolution of a quantum system is unitary, that is, a single (pure) quantum state will remain pure for all times and can never reach a thermal state. Contrary to this theorem, one typically observes quantum many-body systems behave in a thermal way. This paradox has recently become more and more pressing, as isolated quantum systems can be realized in ultracold atomic gases with unprecedented control. This problem is also central for the evolution of the universe as an ideally isolated system. It is closely related to the creation of elementary particles.
In this talk we will review some attempts at resolving the thermalization paradox. As a prototype of an isolated quantum system we will then consider an atomic Bose-Einstein condensate performing Josephson oscillations in a double-well potential trap. We will show that this system thermalizes by a complex dynamics, covered by three different time regimes: an initial period of undamped Josephson oscillations, an intermediate period of avalanche-like creation of bosonic quasiparticles out of the condensate and a slow thermalization regime induced by quasiparticle collisions .
We will draw a detailed analogy to the dynamics of elementary particle creation and thermalization during and after the inflationary phase of of the early universe.