NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2011, 2 (4), P. 32–50
LANDAU-ZENER EFFECT FOR A QUASI-2D PERIODIC SANDWICH
N. Bagraev – A.F.Ioffe Physico-Technical Institute, Russian Academy of Sciences, Saint Petersburg, Russia.
G.Martin – NZ Institute for Advanced study, Massey University, Albany Campus, New Zealand. Professor.
B. S. Pavlov – 1) NZ Institute for Advanced study, Massey University, Albany Campus, New Zealand; 2) V. Fock Institute for Physics at Physical Faculty of the St. Petersburg University, Saint Petersburg, Russia. Professor, DSc., email@example.com.
A. Yafyasov – V. Fock Institute for Physics at Physical Faculty of the St. Petersburg University, Saint Petersburg, Russia. Professor, DSc.
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 multidimensional Schrödinger equations on periodic lattices, because the Cauchy problem is ill-posed for the associated elliptic partial differential equations. In our previous work we suggested a different procedure for the calculation of the Bloch functions for the 2D Schrödinger 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.
Keywords: Landau-Zener effect, Bloch waves.