Applications of Mathematics  June 2007 v52 i3 p267(18)

Stationary Schrodinger equations governing electronic states of quantum dots in the presence of spin-orbit splitting.

AUTHOR(s): Betcke, Marta M.; Voss, Heinrich

AUTHOR ABSTRACT:

In this work we derive a pair of nonlinear eigenvalue problems corresponding to the one-band effective Hamiltonian accounting for the spin-orbit interaction governing the electronic states of a quantum dot. We show that the pair of nonlinear problems allows for the minmax characterization of its eigenvalues under certain conditions which are satisfied for our example of a cylindrical quantum dot and the common InAs/GaAs heterojunction. Exploiting the minmax property we devise an efficient iterative projection method simultaneously handling the pair of nonlinear problems and thereby saving about 25 % of the computation time as compared to the Nonlinear Arnoldi method applied to each of the problems separately.

Keywords: quantum dot, nonlinear eigenvalue problem, minmax characterization, iterative projection method, electronic state, spin orbit interaction

MSC 2000: 65F15, 65F50

Full Text: COPYRIGHT 2007 Springer

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Source Citation: "Stationary Schrodinger equations governing electronic states of quantum dots in the presence of spin-orbit splitting." Applications of Mathematics, June 2007 v52 i3 p267(18). Science Resource Center. Gale. 21 November 2009 <http://galenet.galegroup.com/servlet/SciRC?ste=1&docNum=A168654933>