“…In recent years we have seen a recovering of interest to the Landau-Zener tunneling (LZ-tunneling) in periodic structures. Although this phenomenon was originally discussed with respect to Bloch oscillations (BO) of crystal electrons in a strong electric field [1][2][3][4], nowadays the most successful experimental systems are semiconductor superlattices [5][6][7], one-demensional arrays of optical waveguides [8][9][10][11], and cold atoms in quasi 1D optical lattices [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. These systems allow access to many different aspects of LZ-tunneling including the resonant tunneling [6,13,16,20,23,26], LZ-tunneling in binary (double-periodic) lattices [11,21,22,25], time-resolved LZ-tunneling [15,24], modification of LZ-tunneling by nonlinearity caused by atom-atom interactions [18-20, 22, 23, 26], etc.…”