Analysis and Efficient Solution of Stationary Schrödinger Equation Governing Electronic States of Quantum Dots and Rings in Magnetic Field

Analysis and Efficient Solution of Stationary Schrödinger Equation Governing Electronic States of Quantum Dots and Rings in Magnetic Field

Year:    2012

Communications in Computational Physics, Vol. 11 (2012), Iss. 5 : pp. 1591–1617

Abstract

In this work the one-band effective Hamiltonian governing the electronic states of a quantum dot/ring in a homogenous magnetic field is used to derive a pair/quadruple of nonlinear eigenvalue problems corresponding to different spin orientations and in case of rotational symmetry additionally to quantum number ±ℓ. We show, that each of those pair/quadruple of nonlinear problems allows for the min-max characterization of its eigenvalues under certain conditions, which are satisfied for our examples and the common InAs/GaAs heterojunction. Exploiting the minmax property we devise efficient iterative projection methods simultaneously handling the pair/quadruple of nonlinear problems and thereby saving up to 40% of the computational time as compared to the nonlinear Arnoldi method applied to each of the problems separately. 

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.110910.250511a

Communications in Computational Physics, Vol. 11 (2012), Iss. 5 : pp. 1591–1617

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:   

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