Electronic structure of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mtext>In</mml:mtext></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mtext>Ga</mml:mtext></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:mtext>As</mml:mtext></mml:mrow></mml:math>quantum dots via finite difference time domain method

Ren, GB; Rorison, Judy M

doi:10.1103/physrevb.77.245318

Cited by 9 publications

(5 citation statements)

References 39 publications

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“…5 The use of all forward time-step fourth-order algorithms in solving the imaginary time Schrödinger equation has since been adapted by many research groups. [6][7][8] In principle, the lowest n states of the one-body Schrödinger equation…”

Section: Introductionmentioning

confidence: 99%

Towards DFT Calculations of Metal Clusters in Quantum Fluid Matrices

Chin

Janecek

Krotscheck

et al. 2010

Int. J. Mod. Phys. B

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This paper reports progress on the simulation of metallic clusters embedded in a quantum fluid matrix such as 4 He. In previous work we have reported progress developing a real-space density functional method. The core of the method is a diffusion algorithm that extracts the low-lying eigenfunctions of the Kohn-Sham Hamiltonian by propagating the wave functions (which are represented on a real-space grid) in imaginary time. Due to the diffusion character of the kinetic energy operator in imaginary time, algorithms developed so far are at most fourth order in the time-step. The first part of this paper discusses further progress, in particular we show that for a grid based algorithm, imaginary time propagation of any even order can be devised on the basis of multi-product splitting. The new propagation method is particularly suited for modern parallel computing environments. The second part of this paper addresses a yet unsolved problem, namely a consistent description of the interaction between helium atoms and a metallic cluster that can bridge the whole range from a single atom to a metal. Using a combination of DFT calculations to determine the response of the valence electrons, and phenomenological acounts of Pauli repulsion and short-ranged correlations that are poorly described in DFT, we show how such an interaction can be derived.

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Section: Introductionmentioning

confidence: 99%

Towards DFT Calculations of Metal Clusters in Quantum Fluid Matrices

Chin

Janecek

Krotscheck

et al. 2010

Int. J. Mod. Phys. B

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“…The theoretical understanding on the quantized bound states and the transport properties of QDs is based on the methods of quantum mechanics developed to date, such as perturbation theory with the tight-binding Anderson model [5][6][7], variational calculations [8][9][10], the k•p Hamiltonian method within the envelope-function approximation [11][12][13], density-functional theory [14], mode space approach [15], filter-diagonalization method [16], transmitting boundary method [17,18], numerical coupled-channel method [19], and direct diagonalization techniques in finite difference scheme [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Finite difference method for the arbitrary potential in two dimensions: Application to double/triple quantum dots

Ahn

2014

Superlattices and Microstructures

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A finite difference method (FDM) applicable to a two dimensional (2D) quantum dot was developed as a nonconventional approach to the theoretical understandings of quantum devices. This method can be applied to a realistic potential with an arbitrary shape. Using this method, the Hamiltonian in a tri-diagonal matrix could be obtained from any 2D potential, and the Hamiltonian could be diagonalized numerically for the eigenvalues. The legitimacy of this method was first checked by comparing the results with a finite round well with the analytic solutions. Two truncated harmonic wells were examined as a realistic model potential for lateral double quantum dots (DQDs) and for triple quantum dots (TQDs). The successful applications of the 2D FDM were observed with the entanglements in the DQDs. The level-splitting and anticrossing behaviors of the DQDs could be obtained by varying the distance between the dots and by introducing asymmetry in the well-depths. The 2D FDM results for linear/triangular TQDs were compared with the tight binding approximations.

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“…Among O(N ) methods, we have previously shown that fourth-order imaginary time propagation 2 provides an effective means of solving the Kohn-Sham and related equations 3 . The use of all forward time-step fourth-order algorithms in solving the imaginary time Schrödinger equation has since been adapted by many research groups 4,5,6 . The lowest n states of the one-body Schrödinger equation…”

Section: Introductionmentioning

confidence: 99%

Any order imaginary time propagation method for solving the Schrödinger equation

Chin

Janecek

Krotscheck

2009

Chemical Physics Letters

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The eigenvalue-function pair of the 3D Schrödinger equation can be efficiently computed by use of high order, imaginary time propagators. Due to the diffusion character of the kinetic energy operator in imaginary time, algorithms developed so far are at most fourth-order. In this work, we show that for a grid based algorithm, imaginary time propagation of any even order can be devised on the basis of multi-product splitting. The effectiveness of these algorithms, up to the 12 th order, is demonstrated by computing all 120 eigenstates of a model C60 molecule to very high precisions. The algorithms are particularly useful when implemented on parallel computer architectures.

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Electronic structure ofIn1−xGaxAsquantum dots via finite difference time domain method

Cited by 9 publications

References 39 publications

Towards DFT Calculations of Metal Clusters in Quantum Fluid Matrices

Towards DFT Calculations of Metal Clusters in Quantum Fluid Matrices

Finite difference method for the arbitrary potential in two dimensions: Application to double/triple quantum dots

Any order imaginary time propagation method for solving the Schrödinger equation

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