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Studies of quantum dots: Ab initio coupled-cluster analysis using OpenCL and GPU programming

Christoffer Hirth
Faculty of Mathematics and Natural Sciences, Department of Physics, University of Oslo
University of Oslo, 2012
@article{hirth2012studies,

   title={Studies of quantum dots: Ab initio coupled-cluster analysis using OpenCL and GPU programming},

   author={Hirth, C.},

   year={2012}

}

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Quantum dots, that is, strongly confined electrons, show a variety of interesting properties. Of relevance in both experiments and various technical components, is the possibility to fine tune their electrical and optical properties. Quantum dots can be manufactured by a number of different techniques in practice, but we have in this thesis employed computer simulations to study their properties. In our studies we assume that the confining potential of the quantum dot is a parabolic harmonic oscillator potential, with a confinement strength omega, resulting in a set of basis functions defined by the harmonic oscillator. For more than one electron, we aim at finding the ground-state energy by distributing the electrons in the above mentioned basis states. The coupled-cluster method, widely used in quantum chemistry, atomic, molecular and nuclear physics, is used in this thesis to study ground-state properties of quantum dots. Methods based on constructing many-body correlations starting from a basis of single-particle functions are normally labelled as wave function based methods. Full configuration interation theory and many-body perturbation theory are other examples of widely used wave function based methods, see for example [1]. An important challenge to such methods is to be able to estimate the error made in the calculations, in particular as a function of the truncation in the single-particle basis and truncations in terms of possible many-particle excitations, which effectively limits the number of many-particle states involved in the calculations. In practical calculations the number of included basis functions must be truncated, effectively introducing an error. To understand the convergence of for example various ground state properties in terms of the above truncations, and the possibility to quantify possible errors are central issues in many-body theory.
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