Bose-Einstein Condensation and quasicrystals

Abstract

We consider interacting Bose particles in an external local potential. It is shown that large class of external quasicrystal potentials cannot sustain any type of Bose-Einstein condensates. Accordingly, at spatial dimensions $D\leq 2$ in such quasicrystal potentials a supersolid is not possible via Bose-Einstein condensates at finite temperatures. The latter also hold true for the two-dimensional Fibonacci tiling. However, supersolids do arise at $D\leq 2$ via Bose-Einstein condensates from infinitely long-range, nonlocal interparticle potentials.