Discrete spatial symmetries affect ergodic transport through two-dimensional mesoscopic systems with chaos-inducing geometries and coherence lengths greater than the system's size. This thesis looks at those effects in symmetries both commuting and anticommuting with the current. Additionally the validity of the fractal Weyl law for quantum systems with mixed phase space is examined. Calculating the joint probability distribution of transmission eigenvalues of systems with discrete symmetries using random matrix theory shows that in the orthogonal universality class the transmission eigenvalues show repulsion of every second eigenvalue. For lead-preserving symmetries this behaviour is a result of superposition of independent sequences, while for symmetries mapping leads onto each other different one-point weights in the probability distribution prevent such an interpretation. This has the largest effect for narrow leads, as confirmed by numerical calculations. Microscopical understanding of symmetry effects is gained using a semiclassical approach to calculate the weak localization corrections and universal conductance fluctuations of systems where symmetry is broken by disturbing the internal symmetry of the system or displacing the leads. Duplicating random matrix theory results for perfect symmetry, this approach shows that symmetry effects vanish fast for small deviations from symmetry over a large part of the system while arbitrary deviations with a width smaller than the lead width have finite effect. Symmetry effects will show whenever leads overlap in part with mirrored leads. These results are confirmed with a crossover of random matrix ensembles. We examine the statistics of resonances in open systems with a mixed phase space. For this, we introduce a Husimi representation of decaying states based on the Schur decomposition of the time evolution operator. Applying this method to the open kicked rotator shows that a modified fractal Weyl law holds, which is cormected to emerging quantum-to-classical correspondence.

The current noise properties of a triphenyl molecule bonded between two gold electrodes were studied ~ to determine the suitability of the system as a terahertz radiation source. The system was modelled as a quantum mechanical oscillator coupled to a tunnel junction, and the equation of motion (EOM) for the density matrix of the rotating middle ring of the triphenyl molecule (with the two end-rings frozen), was derived. Weak coupling between the rotating ring and the tunnelling electrons was assumed, as well as a high bias. The EOM allowed the subsequent derivation of an expression for the current noise of the molecular system, which was then analysed numerically. Peaks in the current noise spectrum were observed at 0, 2 and 4 times the rotational frequency of the middle ring, twice the value normally observed for linear coupling between the two systems, a result of the quadratic coupling that was in place. Peak widths of the two lowest frequencies were observed to be narrow, producing a clean signal that is essential for terahertz sources, while the peak heights demonstrated a quadratic dependence on the applied bias V. Investigation of the signal-to-noise ratio (SNR) showed that SNR increased as V increased in magnitude. The SNR was observed to be sizeable for the two lowest frequencies, further illustrating the potential for the triphenyl molecule to be utilised as a terahertz source. The dependence of the SNR and average current on the ratio of the coupling parameters was also investigated, showing that for a fixed ratio of the parameters, where they individually varied by a rescaling factor, the SNR remained constant while the current scaled as the square of the rescaling factor. As the ratio was varied, the SNR and current increased as the magnitude of the ratio tended to zero.

Understanding of how quantum states relate to their environment is vital in order to realize quantum technologies. The class of states possessing the maximum amount of entanglement for a given degree of mixedness is known as maximally entangled mixed states (MEMS). In this Thesis protocols for the generation of these states are studied and their use as teleportation channels is examined. Linking different dimensional systems will prove invaluable to the realization of new quantum technologies. Continuous variable resources are quite favorable for generating entanglement: the transfer of correlations from such resources to discrete systems is studied showing the possibility to engineer the properties of two-qubit states almost at will. Finally this work tackles the crucial problem represented by the detection of entanglement. The larger the entangled state to be detected the more challenging the task becomes. A full characterization of experimentally realizable entanglement witnesses able to discriminate genuinely multipartite entangled states is discussed in detail.

The adsorption and reaction of various simple molecules (O₂, NO, CO and NO₂) commonly associated with gasoline engine exhaust catalysis were investigated on a model catalytic system under ultra-high vacuum conditions using a variety of surface science techniques including molecular beam scattering and temperature programmed desorption. The model catalytic surfaces studied were clean Pt(111), K/Pt(111) and BaO/Pt(111) surfaces. The alkaline and alkaline earth metal surfaces were prepared by metal vapour deposition (in an oxygen background in the case of BaO) and annealing. Also investigated was the ability of each of the catalytic surfaces to oxidise NO and CO and to store and reduce NO₂. It was found that the clean Pt(111) surface was effective at oxidising CO provided the oxygen was in an adsorbed atomic form. Pt(111) was also found to be effective in the reduction of NO₂. NO and O₂ were found to react in a gas phase reaction that made mixed molecular beam studies problematic however it was found when beaming NO with a background pressure of O₂ that no Pt(111) catalysed surface reaction was observed. It was found that dosing K onto the Pt(111) surface increased the sticking coefficient of oxygen greatly and that more than a monolayer of K on the surface catalysed the reduction of NO to N₂. Unlike the Pt(111) surface, K/Pt(111) was capable of storing NO₂ without it being immediately reduced. Potassium peroxide however was found to prevent NO₂ storage. In a similar fashion to K, NO₂ was stored on BaO, being released as NO and O₂ on heating. NO is partially reduced to N₂O by the BaO surface at ambient temperature with increased temperature favouring complete reduction to N₂.

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A computer program for the calculation of molecular orbital self-consistent field (MO-SCF) eigenvalues and eigenvectors of diatomic molecules using the expansion method of Roothaan with Slater-type basis functions is presented. A copy of the program on 105mm microfiche is included in this volume; a listing of the program together with data and program formats and the mode of loading on a modern computer is given in a separate volume. Following a brief discussion of some aspects of Hartree-Fock (HF) theory a conventional SCF program employing the Roothaan Bagus and Jacobi diagonalization procedures is described in Chapter II ; the program employs the Restricted HF open- and closed-shell and the spin-polarized HF formalism. A unified treatment of the one- and two-electron integrals allows their efficient calculation and is the subject of Chapter III; numerical considerations and test values for the required integrals are given in Chapter IV. Chapter V describes the program developed for the formation of the two-electron 'supermatrices'. Minimal basis set test calculations on the ground state and a [3]pi(5o[1]2pi[1]) first excited state of the CO molecule at the experimentally determined equilibrium internuclear distances and suggestions for the improvement and extension of the program are given in Chapter VI. Preliminary calculations on diatomic Ni[2+]0[=] at an internuclear distance of 3. 938 a. u. are reported; the difficulties experienced in obtaining converged solutions with the trial vectors employed are discussed.

This thesis demonstrates the feasibility of producing the first cold source of halogen atoms, using Br atoms as the focus. Br atoms are produced by photodissociation of Br2, and detected by (2+1) REMPI and time-of-flight measurements. Ground- and excited-state Br fragments are formed with a recoil velocity directed along the molecular beam axis. The excess energy from the dissociation laser provides the backscattered Br fragments with sufficient recoil velocity to match and cancel out the average velocity of the molecular beam. The Br fragments which undergo sufficient velocity cancellation remain in the laser detection volume for up to 5 ms. A magnetic trap, composed of two permanent bar magnets with their North poles facing each other, is placed around the detection volume and with an axis perpendicular to the molecular beam and laser axes. The centres of the trap and of the laser interaction volume are overlapped. The magnetic field is linear near the centre of the trap and forms a 3-dimensional well with a depth of 0.22 T, equivalent to a trap depth of U0/kB = 255 mK, with the upper and lower standard error [215,325] mK, for ground-state Br. With this configuration, Br atoms have been detected up to delays of 99 ms, to the next laser pulse, suggesting the possibility of accumulating density over successive molecular beam cycles. The decay of Br atoms from the trap is measured, and a Monte Carlo Markov Chain method is implemented to extract the intensity of the Br signal, which decreases to be on the order of the background noise at delays close to 99 ms. Monte-Carlo simulations demonstrate that the trap loss mechanisms are primarily due to collisions with the molecular beam and background gas, inhibiting the ability to accumulate trap density. These simulations also show that Majorana transitions to higher quantum states are minimal and can be ignored. Experimental measurements confirm that near the peak of the molecular beam, when the strongest signal of Br is observed at long delays, around 60% of initially trapped Br atoms are lost due to molecular beam collisions, and (34 ± 3)% due to collisions with the background gas. To minimise molecular beam collisions, a chopper construct is designed to reduce the beam pulse width and is placed between the molecular beam valve and detection volume. The chopper runs from 3,000 rpm to 80,000 rpm, during which the duration of the molecular beam at the detection volume is shortened from 130 μs (measured at the full width at half maximum) to between 80 μs and 13 μs, respectively. However, the chopper significantly reduces the initial Br2 density in the trapping region, and the influence of the chopper construct in reducing molecular beam collisions requires further experimental work. Further work is also necessary to improve the operational components, such as reducing the base pressure in the detection chamber to lower background gas collisions, or using a heavier carrier gas to increase density of initially trapped Br atoms. These improvements can lead us closer toward building density of cold Br atoms in the trap over successive molecular beam cycles, with which a source of cold, dense halogen atoms can be realised.