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

On the basis of point charge model, we formulate crystalline electronic field (CEF) Hamiltonian HCEF in rare-earth based quasicrystal (QC) and approximant crystal (AC) with ligand ions located at pseudo 5-fold configurations by using operator equivalent method. By setting total angular momentum J = 7/2, CEF quantum critical QC Au51Al34Yb15 1/1 AC Au51Al35Yb14 is analyzed consideration for effec...