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Subject: search.filters.subject.cubic eigenvalue problem

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    Fixed-point methods for a semiconductor quantum dot model
    (2004-09-01)
    Hwang, TM
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    Lin, WW
    ;
    Liu, JL
    ;
    Wang, WC
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    應用數學系
    This paper presents various fixed-point methods for computing the ground state energy and its associated wave function of a semiconductor quantum dot model. The discretization of the three-dimensional Schrodinger equation leads to a large-scale cubic matrix polynomial eigenvalue problem for which the desired eigenvalue is embedded in the interior of the spectrum. The cubic problem is reformulated in several forms so that the desired eigenpair becomes a fixed point of the new formulations. Several algorithms are then proposed for solving the fixed-point problem. Numerical results show that the simple fixed-point method with acceleration schemes can be very efficient and stable. (C) 2004 Elsevier Ltd. All rights reserved.
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    Item type:Item,
    Jacobi-Davidson methods for cubic eigenvalue problems
    (2005-09-01)
    Hwang, TM
    ;
    Lin, WW
    ;
    Liu, JL
    ;
    Wang, WC
    ;
    應用數學系
    Several Jacobi-Davidson type methods are proposed for computing interior eigenpairs of large-scale cubic eigenvalue problems. To successively compute the eigenpairs, a novel explicit non-equivalence deflation method with low-rank updates is developed and analysed. Various techniques such as locking, search direction transformation, restarting, and preconditioning are incorporated into the methods to improve stability and efficiency. A semiconductor quantum dot model is given as an example to illustrate the cubic nature of the eigenvalue system resulting from the finite difference approximation. Numerical results of this model are given to demonstrate the convergence and effectiveness of the methods. Comparison results are also provided to indicate advantages and disadvantages among the various methods. Copyright (c) 2004 John Wiley & Sons, Ltd.
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    A model for semiconductor quantum dot molecule based on the current spin density functional theory
    (2006-11-01)
    Liu, Jinn-Liang
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    Chen, Jen-Hao
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    Voskoboynikov, O.
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    應用數學系
    ;
    電子工程學系及電子研究所
    Based on the current spin density functional theory, a theoretical model of three vertically aligned semiconductor quantum dots is proposed and numerically studied. This quantum dot molecule (QDM) model is treated with realistic hard-wall confinement potential and external magnetic field in three-dimensional setting. Using the effective-mass approximation with band nonparabolicity, the many-body Hamiltonian results in a cubic eigenvalue problem from a finite difference discretization. A self-consistent algorithm for solving the Schrodinger-Poisson system by using the Jacobi-Davidson method and GMRES is given to illustrate the Kohn-Sham orbitals and energies of six electrons in the molecule with some magnetic fields. It is shown that the six electrons residing in the central dot at zero magnetic field can be changed to such that each dot contains two electrons with some feasible magnetic field. The Forster-Dexter resonant energy transfer may therefore be generated by two individual QDMs. This may motivate a new paradigm of Fermionic qubits for quantum computing in solid-state systems. (C) 2006 Elsevier B.V. All rights reserved.