Decreasing critical temperature of gas BEC in spatially periodic potential and relevance to experiments treated by Mott-Hubbard model

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It is shown that the critical temperature of gas Bose-Einstein condensation decreases in deepening periodic potential, in contrast to common regularity in a separate potential well. The physical explanation of this phenomenon is given. Characteristic scale of potential energies decaying the critical temperature is the quantum recoil energy of periodic potential. The theory represents an alternative and direct approach to the experimental results (C.Orzel et al Science 291, 2386 (2001); M.Greiner et al, Nature 415, 39 (2002)) obtained with BEC in optical lattices and treated as the phase squeezing or Mott transition processes.