Landau-Zener effect for a quasi-2D periodic sandwich
Аннотация
Bloch-waves in 1D periodic lattices are typically constructed based on the transfer-matrix approach, with a complete system of solutions of the Cauchy problem on a period. This approach fails for the multi-dimensional Schr¨odinger equations on periodic lattices, because the Cauchy problem is ill-posed for the associated elliptic partial differential equations. In our previous work [8] we suggested a different procedure for the calculation of the Bloch functions for the 2D Schr¨odinger equation based on the Dirichlet-to-Neumann map substituted for the transfer -matrix. In this paper we suggest a method of calculation of the dispersion function and Bloch waves of quasi-2D periodic lattices, in particular of a quasi-2D sandwich, based on construction of a fitted solvable model.
Об авторах
N. Bagraev
A. F. Ioffe Physico-Technical Institute, Russian Academy of Sciences
Россия
Россия
G. Martin
Massey University, Albany Campus
Новая Зеландия
Новая Зеландия
B. Pavlov
Massey University, Albany Campus; St. Petersburg University
Россия
Россия
A. Yafyasov
St. Petersburg University
Россия
Россия
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Рецензия
Для цитирования:
, , , . Наносистемы: физика, химия, математика. 2011;2(4):32-50.
For citation:
Bagraev N., Martin G., Pavlov B.S., Yafyasov A. Landau-Zener effect for a quasi-2D periodic sandwich. Nanosystems: Physics, Chemistry, Mathematics. 2011;2(4):32-50.
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