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Analysis And Efficient Solution Of Stationary Schrödinger Equation Governing Electronic States Of Quantum Dots And Rings In Magnetic Field

Published online by Cambridge University Press:  20 August 2015

Marta M. Betcke  and
Heinrich Voss
Marta M. Betcke*
Affiliation:
Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK
Heinrich Voss*
Affiliation:
Institute of Numerical Simulation, Hamburg University of Technology, D-21071 Hamburg, Germany
*
Corresponding author.Email:[email protected]
Email:[email protected]
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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•i. 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.

Keywords

65F1565F50Quantum dotquantum ringnonlinear eigenvalue problemminmax characterizationiterative projection methodelectronic statespin orbit interactionmagnetic field
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 5 , May 2012 , pp. 1591 - 1617
Copyright
Copyright © Global Science Press Limited 2012

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