Keeling11a

Exciton-polariton condensation. J. Keeling and N. G. Berloff in Contemp. Phys. 52:131 (2011).  What the paper says!?

This page is still in progress.

we do not discuss theoretical techniques, but we will try to make connections between the behaviour of the polariton system and other well-studied fields, such as quantum hydrody namics [15–17], lasing [18,19], and nonlinear optics and pattern formation [20,21]. Furthermore, by arranging our discussion according to phenomena, we will not discuss the historical development of the subject.

There is a nice discussion of ODLRO from the reduced density matrix. Although this needs clarifications, e.g., on statements such as:

When condensed, one eigenvalue becomes macroscopic, indicating that many particles are in the same state.

See in particular their Refs. [23,24] on symmetry breaking and emergence of classical fields.

Interesting observation that strong interactions are actually detrimental to condensation:

The require ment of weak interaction is essential here, since in a strongly interacting system it is impossible to divide single-particle modes into highly occupied and practi cally empty ones: these modes are always coupled to the rest of the system.

This statement is dubious:

The existence of long-range phase coherence is also associated with the idea of breaking of phase symmetry. This is because in the condensed state a large number of particles occupy the same quantum state, and so it is possible to see macroscopic interference effects, meaning that a well-defined quantum mechanical phase can exist.

Nice summary on phase properties in relation to «the motion of point vortices and vortex lines in classical Eulerian fluid»

One particularly notable feature of BEC is that the many particle quantum system can be represented by a classical complex-valued field $\Psi$, so the dynamics of the system can be described by essentially classical equations of nonlinear physics.