One question I want to raise concerns the influence of disorder on
quantum phase transitions, in particular in metallic systems. This
question has an experimental and a theoretical aspect:
(i) In the existing and maybe new experiments, can one identify robust,
universal disorder effects associated with the quantum phase transition
(by robust and universal I mean something like the weak localization
effects in doped semiconductors which are observed over an extremely
broad range of systems)
(ii) Concerning theory, the big question is how to attack a dirty, metallic
quantum phase transition. The traditional perturbative approach probably
fails because it misses the rare region effects which seem to dominate the
physics. No other systematic approach exists so far.


The second question I want to raise is:
What happens to a quantum phase transition in a non-equilibrium situation?
Imagine, e.g., a ferromagnetic quantum phase transition in the presence of
an electric current. Will the current just slightly heat up the sample?
Experience with classical non-equilibrium transitions suggests that much
interesting things could happen, such long-range correlations produced by the
currents could completely change the character of the transition.