The dispersion functions for quasi-2D periodic lattices via Dirichlet-to-Neumann map

2nd International Conference on Mathematical Modeling in Physical Sciences 2013

物理学;数学

Goncharov, L.^1 ; Yafyasov, A.^1 ; Pavlov, B.S.^1,2 ; Martin, G.J.^1,2

Physical Faculty, St.Petersburg State University, 2 Ulyanovskaya st., Petrodvorets, St.Petersburg, 198504, Russia^1

New Zealand Institute of Advanced Study, Massey University, 12 Oteha Rhoe, Albany, 0745, Auckland, New Zealand^2

关键词: Computational resources;    Dirichlet-to-Neumann map;    Dispersion relations;    Finite element solution;    Infinite dimensional;    Numerical calculation;    Quantum-scattering theory;    Quasi periodic boundary condition;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/490/1/012237/pdf
DOI  :  10.1088/1742-6596/490/1/012237

来源: IOP

【 摘 要 】

Dirichlet-to-Neumann map is a powerful mathematical instrument that has proved to be useful in the analysis of the 2D and 3D solid state structures when described by the Schrodinger equation. In this paper we apply the DN-map approach to the analysis and numerical calculation of the dispersion relation for periodic quasi-2D layers constructed with unit 3D cells. Basically the dispersion relation is obtained using the methods of quantum scattering theory. The infinite-dimensional matching problem on the interfaces of the cells will be replaced by a finite-dimensional contact subspace that can always be selected so as to provide sufficient accuracy for the calculation of the dispersion relation. The techniques we present also require less computational resource than that of the direct finite-element solution of the Schrodinger equation with quasi-periodic boundary condition.