Landau-Zener effect for a quasi-2D periodic sandwich
Abstract
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.
Supporting agencies: Authors are grateful to the Marsden Fund of the Royal Society of New Zealand for a generous support which allowed the personal contacts of our team over the mountains and across the oceans. One of authors (B.P.) is grateful to the Russian Academy for the support from the grant RFBR 03-01-00090.
About the Authors
N. Bagraev
A. F. Ioffe Physico-Technical Institute, Russian Academy of Sciences
Russian Federation
Russian Federation
St. Petersburg
G. Martin
Massey University, Albany Campus
New Zealand
New Zealand
Professor, NZ Institute for Advanced study
B. S. Pavlov
Massey University, Albany Campus; St. Petersburg University
Russian Federation
Russian Federation
Professor, DSc., NZ Institute for Advanced study; V. Fock Institute for Physics at Physical Faculty
Saint Petersburg
A. Yafyasov
St. Petersburg University
Russian Federation
Russian Federation
Professor, DScV, Fock Institute for Physics at Physical Faculty
Saint Petersburg
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Review
For citations:
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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