### 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).