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João Lourenço, Diogo Sousa, Bruno Teixeira, Ricardo Dias (2011)
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Nanoscale Systems: Mathematical Modeling, Theory and Applications
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Within the effective mass and nonparabolic band theory, a general framework of mathematical models and numerical methods is developed for theoretical studies of semiconductor quantum dots. It includes single-electron models and many-electron models of Hartree-Fock, configuration interaction, and current-spin density functional theory approaches. These models result in nonlinear eigenvalue problems from a suitable discretization. Cubic and quintic Jacobi-Davidson methods of block or nonblock...