In this work the Path Integral quantum Monte Carlo (PI-QMC) method has been used to study exciton complexes in semiconductor nanostructures. This powerful technique allows for coulomb correlations in these complexes to be correctly treated, and at the same time allowing for nite temperature simulations in an arbitrary external potential without the need for complicated trial function or basis set information. Quantum dots and rings were modelled using both analytic potentials, and by potentials derived from atomistic models of these structures, including strain and piezoelectric e ects. The e ect of strain and the piezoelectric potential on quantum rings is explored, and rings are shown to have a unique strain and piezoelectric pro le which directly impacts observables. This unique piezoelectric potential in quantum rings is exploited by use of vertical electric elds, to induce a novel lateral switching of the exciton and biexciton probability distributions when the direction of the applied eld is switched. Calculations of in-plane polarizability suggest the switching would be observable experimentally. The diamagnetic susceptibility of quantum rings and dots are investigated, and accurate reproduction of experimental results are shown { which require the proper treatment of coulomb correlations. Finally, the transition between a bound and anti-bound biexciton in a core/shell Type-II colloidal quantum dot, with increasing shell thickness is for the rst time theoretically shown. Excellent agreement with experimental results are seen, and these results are contrasted with previous perturbative results which miss this transition from the literature.

A method for computing electron momentum densities and Compton profiles from ab initio calculations is presented. This is employed, together with the momentum density spectroscopy known as Compton scattering to investigate the electronic structure of MgCNi3. A method for computing the positron state within a material is also presented. In our method for computing the electron momentum density, reciprocal space is divided into optimally-shaped tetrahedra for interpolation, and the linear tetrahedron method is used to obtain the momentum density and its projections such as Compton profiles. Results are presented and evaluated against experimental data, showing good agreement, and demonstrating the accuracy of our method. For the intermetallic superconductor MgCNi3 , high-resolution x-ray Compton scattering experiments were combined with electronic structure calculations to study a sample with the composition MgCO.93 Ni2.85. Our calculations indicate that the electronic structure, whilst smeared by disorder, does not drastically change in the presence of vacancies, and provide an explanation for some of the discrepancies between measurements of single crystals and polycrystals. Compton scattering measurements were used to determine a Fermi surface in good agreement with that of our supercell calculation, establishing the presence of the hole and electron Fermi surface sheets that are necessary for the proposed two-gap model for the superconductivity. We identify significant smearing of certain parts of the Fermi surface when C and Ni vacancies are present. To calculate the positron state, we have implemented two component density functional theory in the limit of vanishing positron density. We present calculations of the positron lifetime, affinity, and of the momentum density of annihilating electron-positron pairs, for several materials, using a wide variety of electron-positron correlation and enhancement schemes, finding excellent agreement with previous calculations and experimental results. Possible limitations of the method are found in describing positrons localised in vacancies .

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This thesis investigates the properties of entanglement in one-dimensional many-body systems. In the first part, the non-equilibrium dynamics following a sudden global quench are exploited for the purpose of generating long-range entanglement. A number of initial states are considered. It is shown that the dynamics following the considered quench can be mapped to the problem of a state transfer. The quench can then be optimised by exploiting the literature about quantum state transfer to generate maximal long-range entanglement and maximal block entropy. In the second part of the thesis, a spin chain emulation of the two-channel, Kondo (2CK) model is proposed. Studying the local magnetisation and susceptibility we show that the spin-only emulation truly represent the two-channel Kondo model and extract the Kondo temperature. A detailed entanglement analysis is presented. Using density matrix renormalisation group (DMRG), which allow for real space analysis, Kondo temperature and Kondo length are evaluated. An entanglement measure, namely the negativity, as well as the Schmidt gap are used as possible order parameters predicting the critical point. An extensive analysis of the block entropy of the system is presented for different limiting values of Kondo coupling. A universal scaling of the impurity contribution to the entropy is found and the 2CK residual entropy is extracted. The last part explores quench dynamics in Kondo systems using time-dependent DMRG. For a quench in the Kondo coupling a travelling and breathing clouds are ob-served. A measurement-induced dynamics lead to an oscillation between an effective singlet and triplet states of the impurity and the Kondo cloud. Kondo temperature can be extracted from the frequency of the oscillation.

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Dilute magnetic semiconductors (DMSs) are ideal candidates for spintronic devices as they exhibit both semiconducting and magnetic properties. The defining feature of a DMS material is the exchange interactions between the magnetic ions and the band electrons and holes, which leads to many of the spin behaviours observed. A fundamental property of DMSs is that a relatively small external magnetic field can cause enormous Zeeman splittings of the electronic energy levels, which allows separating of states with different spins. The giant Zeeman effect present in the DMS systems also leads to the possibility of trapping quasiparticles in an inhomogeneous magnetic field. In this thesis the effect of inhomogeneous magnetic fields on excitons in a DMS quantum well is investigated. We look at the possibility of trapping excitons in hybrid structures composed of a DMS quantum well placed a few nanometres below a nanoscale and microscale ferromagnetic disk and a ferromagnetic strip. Quasiparticles in a DMS quantum well are shown to undergo a splitting between band states for different spin components due to the giant Zeeman interaction. Due to the inhomogeneous magnetic field created by a nanoscale ferromagnetic disk in the vortex state the quasiparticles are found to be confined in a small region on the quantum well. The behaviours of excitons in the presence of both a homogeneous and inhomogeneous magnetic field is then discussed. The binding energy of a heavy hole exciton in a finite DMS quantum well in the presence of a homogeneous is calculated. The study is extended to look at excitons in the presence of an inhomogeneous magnetic field. The behaviour of excitons in the presence of a inhomogeneous magnetic field, is found to depend on the type of magnetic field, and is shown to be different for a magnetic field created by a microscale and nanoscale ferromagnetic disk and a ferromagnetic strip.

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