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Near absolute zero, some materials are superconductors. Other materials are superfluids. Others are Bose-Einstein Condensates.

Is there a complete list of possibilities? Or is this still a research topic?

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Actually, superfluidity is describable as Bose-Einstein condensation of bosonic atoms. Superconductors are slightly more complex. Type-I superconductors are well-described by a model in which the electrons (which are fermions) form bosonic pairs which then form a Bose-Einstein condensate. So these three are connected to some extent. All of this on a sidenote.

This certainly still is an active research topic. For example, another possible state of matter was discovered not too long ago: supersolids. I believe the existence of this state is still disputed and I am sure there is no explanation that acounts for all of its properties and behaviour yet.

For a complete list I suggest you take a look at the wikipedia page for states of matter as well as the one for topological order, which is a new kind of order based on topological properties of matter. There is also some useful information on the latter on this physics.se page: Topological phase.

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You forgot the active research on topological phase of matter, too, and all the properties of emerging field at low temperatures: how to create relativistic quantum field in a lab. With the Bose-Einstein condensation, one can separate the phase of matter as follow: i) the wave functions strongly overlap (degenerate Bose gas) ii) the wave functions are organized in term of symmetry (solid system, with its own classification in term of symmetry) iii) the wave functions are organized, but don't speak to each other (liquid) and finally iv) the wave functions do not interact at all (gas) –  FraSchelle Dec 9 '12 at 17:32
When the wave functions overlap strongly, one recover in some sense some notion of continuity that we may think we lost in a solid phase (because the atoms in lattice are somehow discrete). This allows to classify more precisely the pure quantum state of matter in term of topology: the wave function are so entangled that they acquire a new macroscopic behavior (roughly speaking). Check for topological order on this site for more infos. –  FraSchelle Dec 9 '12 at 17:36
Thanks for the addition, I didn't think of that when I was writing my answer. –  Wouter Dec 9 '12 at 17:41
No problem. That's the meaning of this site to have more than one people answering. Thanks anyway for the update in your answer. –  FraSchelle Dec 9 '12 at 17:57
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