On the effects of localisation on Bose Einstein Condensation.
Jaeck Thomas,
(School of Mathematical Sciences, University College Dublin, Ireland)
jueves 10 de junio de 2010
Abstract: Bose Einstein condensation (BEC) in translation invariant systems is known to occur only in dimension 3 or higher. However, it is possible to trigger condensation in low dimensional systems by adding an external potential able to make the system "localised" (and hence, breaking the translation invariance). But the condensates obtained in that way are to be found a priori in localised eigenstates, while BEC is generally believed to be occuring in kinetic energy eigenstates (plane waves). For a class of random external potentials or weak (scaled) potentials, we show that these two phenomena are equivalent if one restricts ourselves to the concept of generalised BEC, that is condensation on a narrow band of energy instead of a single state. We then study the occupation of single kinetic eigenstate, and show that localisation prevents the condensate to appear in any of them, even though generalised BEC does occur.