THEORETICAL-STUDY OF LANDAU-ZENER TUNNELING AT THE M-CROSSING(N LEVEL)

Two rules have been analytically obtained for the well-known problem o f Landau-Zener tunneling at the M+N level crossing. Both rules are val id for the arbitrary crossing rate, level splitting vectors, and mixin g matrix. The first rule is given by a simple expression for an arbitr ary diagonal element of the S matrix. The second rule is that the S ma trix has (M-1) x (M-1) and (N-1) x (N-1) triangles of zeros in its M x M and NXN submatrices, i.e., some interlevel transitions are strictly forbidden. Some other features of the off-diagonal elements are also studied, using a 2+2 level crossing as an example. Numerical and analy tical results of the 2+2 crossing show difference from a 1+2 level, an d we conclude that the M+N level crossing cannot be expressed as a mer e composition of 1+1 level crossings except for the above two rules. F inally we discuss the possibility of a single-electron operation using these results.