I'm currently at a workshop on quantum impurity problems in nanostructures and molecular systems, sponsored by the Max Planck Institute for Complex Systems here in Dresden. A quantum impurity problem is defined by a localized subsystem (the impurity) with some specific quantum numbers (e.g. charge; spin) coupled to nonlocal degrees of freedom (e.g. a sea of delocalized conduction electrons; spin waves; phonons). The whole coupled system of impurity (or impurities) + environment can have extremely rich properties that are very challenging to deduce, even if the individual subsystems are relatively simple.
A classic example is the Kondo problem, with a localized impurity site coupled via tunneling to ordinary conduction electrons. The Coulomb repulsion is strong enough that the local site can really be occupied by only one electron at a time. However, the total energy of the system can be reduced if the localized electron can undergo high order virtual processes where it can pop into the conduction electron sea and back. The result is an effective magnetic exchange between the impurity site and the conduction electrons, as well as an enhanced density of states at the Fermi level for the conduction electrons. The ground state of this coupled system involves correlations between many electrons, and results in a net spin singlet. The Kondo problem can't be solved by perturbation theory, like many impurity problems.
The point is, with nanostructures it is now possible to implement all kinds of impurity problems experimentally. What is really exciting is the prospect of using these kinds of tunable model systems to study strong correlation physics (e.g. quantum phase transitions in heavy fermion compounds; non-Fermi liquid "bad metals") in a very controlled setting, or in regimes that are otherwise hard to probe (e.g., impurities driven out of equilibrium). This workshop is about 70 or 80 people, a mix of theorists and experimentalists, all interested in this stuff. When I get back I'll highlight a couple of the talks.