Epitaxially grown quantum dots (QDs) make up a significant portion of nanoscale semiconductor research, yet precise solutions for their eigenstates in complex geometries are often unknown. Eigenstates are extremely relevant as they impact the emission wavelength, performance, and stability of many optoelectronic devices. In this thesis, atomic force microscopy, transmission electron microscopy, and atom probe tomography (APT) are used to assess and compare QD size and core concentration. APT by means of isosurface reconstruction provides the most accurate ensemble averaged quantum dot size and core concentration. High-angle annular dark-field imaging quantifies core concentration very well, but fails in comparison to precisely quantify QD size. Ensemble averaging is discarded in favour of using the raw APT data to devise a model that can solve the Schrödinger equation in 3-dimensional space and can be expanded upon to include non-trivial quantum dot geometries of any kind. The electron and hole eigenstates for an entire quantum dot ensemble are solved using this model. Hybridized eigenstates between neighbouring quantum dots are realized and found to experience both bonding and anti-bonding of the charge carriers. The existence of a degenerate state is also discovered. The simulated eigenenergies are compared to the photoluminescence emission spectrum and found to accurately represent the exciton recombination energy. This makes it possible to obtain very realistic 3-D eigenstate representations for a variety of complex structures. The modelling technique outlined in this thesis is not constrained to just QDs, but can also be applied to an array of many other nanoscale structures. / Thesis / Master of Applied Science (MASc)

Using the idea that a quantum mechanical system drops to its ground state as its temperature goes to absolute zero several operators are devised to enable the approximation of the lowest order energy eigenstate of a given symmetry; as well as an approximation to the energy eigenvalue of the same order.

Many quantum computation algorithms, and processes like measurement based quantum computing, require the initial state of the quantum computer to be an eigenstate of a specific unitary operator. Here we study how quantum states that are eigenstates of finite dimensional irreducible representations of the special unitary (SU(d)) and the permutation (S_n) groups can be efficiently constructed in the computational basis formed by tensor products of the qudit states. The procedure is a unitary transform, which first uses Schur-Weyl duality to map every eigenstate to a unique Schur basis state, and then recursively uses the Clebsch - Gordan transform to rotate the Schur basis state to the computational basis. We explicitly provide an efficient quantum algorithm, and the corresponding quantum logic circuit, to generate any desired eigenstate of SU(2) and SU(3) irreducible representations in the computational basis.

No description available.

In der vorliegenden Arbeit wird die Fredholm-Methode zur semiklassischen Berechnung einzelner Eigenzustaende von Quantenabbildungen eingesetzt. Es wird gezeigt, wie auch Eigenzustaende zu entarteten Eigenwerten berechnet werden koennen. Die semiklassische Berechnung eines Eigenzustandes erfolgt mittels der Husimifunktion. Es wird gezeigt, wie das Auftreten von Bifurkationen periodischer Bahnen beruecksichtigt werden kann. Dies geschieht auch fuer den Fall von energiegemittelten Eigenzustaenden. Ebenfalls wird die Stoerung einer Quantenabbildung durch einen Punktstreuer und dessen Auswirkungen auf die semiklassische Berechnungen untersucht.

The first part of the present Phd thesis is devoted to transport investigations in disordered quantum systems. We aim at quantitatively determining transport parameters like conductivity, mean free path, etc., for simple models of spatially disordered and/or percolated quantum systems in the limit of high temperatures and low fillings using linear response theory. We find the transport behavior for some models to be in accord with a Boltzmann equation, i.e., long mean free paths, exponentially decaying currents although there are no band-structures to start from, while this does not apply to other models even though they are also almost completely delocalized. The second part of the present PhD thesis addresses the issue of initial state independence (ISI) in closed quantum system. The relevance of the eigenstate thermalization hypothesis (ETH) for the emergence of ISI equilibration is to some extent addressed. To this end, we investigate the Heisenberg spin-ladder and check the validity of the ETH for the energy difference operator by examining the scaling behavior of the corresponding ETH-fluctuations, which we compute using an innovative numerical method based on typicality related arguments. While, the ETH turns out to hold for the generic non-integrable models and may therefore serve as the key mechanism for ISI for this cases, it does not hold for the integrable Heisenberg-chain. However, close analysis on the dynamic of substantially out-of-equilibrium initial states indicates the occurrence of ISI equillibration in the thermodynamic limit regardless of whether the ETH is violated. Thus, we introduce a new parameter $v$, which we propose as an alternative of the ETH to indicate ISI equillibration in cases, in which the ETH does not strictly apply.

In der vorliegenden Arbeit wird die Fredholm-Methode zur semiklassischen Berechnung einzelner Eigenzustaende von Quantenabbildungen eingesetzt. Es wird gezeigt, wie auch Eigenzustaende zu entarteten Eigenwerten berechnet werden koennen. Die semiklassische Berechnung eines Eigenzustandes erfolgt mittels der Husimifunktion. Es wird gezeigt, wie das Auftreten von Bifurkationen periodischer Bahnen beruecksichtigt werden kann. Dies geschieht auch fuer den Fall von energiegemittelten Eigenzustaenden. Ebenfalls wird die Stoerung einer Quantenabbildung durch einen Punktstreuer und dessen Auswirkungen auf die semiklassische Berechnungen untersucht.