Thermodynamic behavior from Schroedingers dynamics in incompletely observed quantum systems

Jochen Gemmer, FB Physik, Universität Osnabrück

Thermodynamic behavior is characterized by the approach to equilibrium as stated by the second law. The Schroedinger equation, however, neither features any fixpoint nor does it allow for a change of entropy with respect to the full system. This raises the question how quantum systems can, in general, exhibit thermodynamic behavior. We basically consider two scenarios:
i) Quantum systems coupled to other (larger) quantum systems which need not to be reservoirs in the traditional sense. The observation is incomplete since only observables corresponding to the primary system are considered.
ii) Interacting quantum systems placed on a (finite) lattice. Only the particle number or the energy at each site is observed. This allows for an investigation of the possible emergence of diffusion from Schrödingers dynamics.
In both scenarios thermodynamic behavior with respect to the considered observables is found. Key concepts are entanglement, projection techniques and the Hilbert Space Average Method (HAM).