Theory of Critical Temperature Adiabatic Change for Ideal Gas   Bose-Einstein Condensation in Optical Lattices
  We present a scheme of analytical calculations determining the critical temperature and the number of condensed atoms of ideal gas Bose-Einstein condensation in external potentials with 1D, 2D or 3D periodicity. In particular we show that the width of the lowest energy band appears as the main parameter determining the critical temperature of condensation. Is obtained a very simple, proportional to 1/3 degree, regularity for this dependence. The fundamental role of tunneling in physics of condensate establishment is underscored. 
G.A. Muradyan and A.Zh. Muradyan