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...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 minmax 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.展开更多
基金We would like to thank Oleksandr Voskoboynikov for his comments on the physical relevance of the model under consideration.We also thank the anonymous referees for their comments helping us to improve this manuscript.
文摘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 minmax 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.
