This thesis focuses on the interplay of the spin-orbit coupling, the electronic correlations and the bandwidth energy scales, along with the lattice distortions seen in perovskite iridates. In particular, we study the magnetic phases in these materials and the insulator to metal transition that occurs as the dimensionality of the system is changed. Motivated by the novel magnetic phases seen in the Sr2IrO4 system, we study the band structures of three materials in the Sr(n+1)Ir(n)O(3n+1) Ruddlesden-Popper series by use of a tight-binding model. From the effect of spin-orbit coupling, we see that the relevant bands near the Fermi energy are indeed made of effective J=1/2 states. This spin-orbit separation of the bands creates effectively smaller bandwidth which can then be split via magnetic ordering driven by electronic correlations. By the use of a self-consistent mean-field theory, we derive the ordering for each of the three materials studied and show that the nature of the magnetic ordering is highly dependent on the lattice structure. The ordering in the bilayer Sr3Ir2O7, which has been a topic of debate in recent experimental studies, is understood within the current approach to be a collinear antiferromagnetic order, in agreement with the latest results. Given that the iridate systems have large spin-orbit coupling, and that the topic of topological insulators has become a very popular subject of research, we discuss the proximity of the perovskite iridates to topological insulators. Since the SrIrO3 material displays a semimetal structure with nodal dispersion near the Fermi level, we looked at an extra term in the Hamiltonian that could lift the nodal lines and turn the system into an insulator. Further studies of the parity eigenvalues of the bands at each time reversal invariant momentum point confirms that for a range of this extra term, a topological phase can be achieved. A discussion on material realization of such a phase is also given where we suggest that a Sr2IrRhO6 superstructure might be a good candidate to achieve this state.

This study investigates the possibility of fabricating periodic cellular materials (PCMs) via the lost foam casting (LFC) process using aluminum alloy A356 and magnesium alloy AZ91. This approach combines the structural efficiency of PCM architectures with the processing advantages of near-net-shape LFC. An initial feasibility study fabricated corrugated A356 panels. This was followed by a study of casting variables such as pattern design, vacuum assistance, and alloying additions in order to improve the fillability of the small cross-section struts. Finally, integrated pyramidal sandwich panels having different relative densities were subjected to artificial aging treatments and subsequently tested in uniaxial compression. The A356 PCMs experienced a continuous increase after yielding while the AZ91 PCMs exhibited strut fracture after peak strength. The results showed the compressive yield strengths of this study are comparable with those previously reported PCMs produced by different fabrication methods.

Lattice-Reduction has become a popular way of improving the performance of MIMO detectors. However, developing an efficient high-throughput VLSI implementation of LR has been a major challenge in the literature. This thesis proposes a hardware-optimized version of the popular LLL algorithm that reduces its complexity by 70% and achieves a fixed runtime while maintaining ML diversity. The proposed algorithm is implemented for 4x4 MIMO systems and uses a novel pipelined architecture that achieves a fixed low processing latency of 40 cycles, resulting in a fixed throughput that is independent of the channel correlation. The proposed LR core, fabricated in 0.13um CMOS, is the first fabricated and tested LR ASIC implementation in the literature. Test results show that the LR core achieves a maximum clock rate of 204 MHz, yielding a throughput of 510 Mbps, thus satisfying the aggressive throughput requirements of emerging 4G wireless standards, such as IEEE-802.16m and LTE-Advanced.

This thesis focuses on the interplay of the spin-orbit coupling, the electronic correlations and the bandwidth energy scales, along with the lattice distortions seen in perovskite iridates. In particular, we study the magnetic phases in these materials and the insulator to metal transition that occurs as the dimensionality of the system is changed. Motivated by the novel magnetic phases seen in the Sr2IrO4 system, we study the band structures of three materials in the Sr(n+1)Ir(n)O(3n+1) Ruddlesden-Popper series by use of a tight-binding model. From the effect of spin-orbit coupling, we see that the relevant bands near the Fermi energy are indeed made of effective J=1/2 states. This spin-orbit separation of the bands creates effectively smaller bandwidth which can then be split via magnetic ordering driven by electronic correlations. By the use of a self-consistent mean-field theory, we derive the ordering for each of the three materials studied and show that the nature of the magnetic ordering is highly dependent on the lattice structure. The ordering in the bilayer Sr3Ir2O7, which has been a topic of debate in recent experimental studies, is understood within the current approach to be a collinear antiferromagnetic order, in agreement with the latest results. Given that the iridate systems have large spin-orbit coupling, and that the topic of topological insulators has become a very popular subject of research, we discuss the proximity of the perovskite iridates to topological insulators. Since the SrIrO3 material displays a semimetal structure with nodal dispersion near the Fermi level, we looked at an extra term in the Hamiltonian that could lift the nodal lines and turn the system into an insulator. Further studies of the parity eigenvalues of the bands at each time reversal invariant momentum point confirms that for a range of this extra term, a topological phase can be achieved. A discussion on material realization of such a phase is also given where we suggest that a Sr2IrRhO6 superstructure might be a good candidate to achieve this state.

This study investigates the possibility of fabricating periodic cellular materials (PCMs) via the lost foam casting (LFC) process using aluminum alloy A356 and magnesium alloy AZ91. This approach combines the structural efficiency of PCM architectures with the processing advantages of near-net-shape LFC. An initial feasibility study fabricated corrugated A356 panels. This was followed by a study of casting variables such as pattern design, vacuum assistance, and alloying additions in order to improve the fillability of the small cross-section struts. Finally, integrated pyramidal sandwich panels having different relative densities were subjected to artificial aging treatments and subsequently tested in uniaxial compression. The A356 PCMs experienced a continuous increase after yielding while the AZ91 PCMs exhibited strut fracture after peak strength. The results showed the compressive yield strengths of this study are comparable with those previously reported PCMs produced by different fabrication methods.

Lattice-Reduction has become a popular way of improving the performance of MIMO detectors. However, developing an efficient high-throughput VLSI implementation of LR has been a major challenge in the literature. This thesis proposes a hardware-optimized version of the popular LLL algorithm that reduces its complexity by 70% and achieves a fixed runtime while maintaining ML diversity. The proposed algorithm is implemented for 4x4 MIMO systems and uses a novel pipelined architecture that achieves a fixed low processing latency of 40 cycles, resulting in a fixed throughput that is independent of the channel correlation. The proposed LR core, fabricated in 0.13um CMOS, is the first fabricated and tested LR ASIC implementation in the literature. Test results show that the LR core achieves a maximum clock rate of 204 MHz, yielding a throughput of 510 Mbps, thus satisfying the aggressive throughput requirements of emerging 4G wireless standards, such as IEEE-802.16m and LTE-Advanced.

Quantum information is a growing field showing exciting possibilities for computational speed-up and communications. For the successful implementation of quantum computers, high-precision control is required to reach fault-tolerant thresholds. Control of quantum systems pertains to the manipulation of states and their evolution. In order to minimize the effects of the environment on the control operations of the qubits, control pulses should be made time-optimal. In addition, control pulses should be made robust to noise in the system, dispersion in energies and coupling elements, and uncertain parameters. In this thesis, we examine a robust time-optimal gradient ascent technique which is used to develop controls of the motional degrees of freedom for an ensemble of neutral atoms in a one-dimensional optical lattice in the high dispersion regime with shallow trapping potentials. As such, the system is analyzed in the delocalized basis. The system is treated as an ensemble of atoms with a range of possible quasimomenta across the first Brillouin zone. This gives the ensemble of Hamiltonians, indexed by the quasimomenta, a distinct spectra in their motional states and highly inhomogeneous control Hamiltonians. Thus, the optical lattice is seen as a model system for robust control. We find optimized control pulses designed using an ensemble modification of gradient-ascent pulse engineering robust to any range of quasimomentum. We show that it is possible to produce rotation controls with fidelities above 90\% for half of the first Brillouin zone with gate times in the order of several free oscillations. This is possible for a spectrum that shows upwards of 75\% dispersion in the energies of the band structure. We also show that NOT controls for qubit rotations on the entire Brillouin zone fidelities above 99\% were possible for 0.6\% dispersion in energies. The gate times were also in the order of several free oscillations. It is shown that these solutions are palindromic in time due to phase differences in some of the energy couplings when comparing one half of the Brillouin zone to another. We explore the limits of discretized sampling of a continuous ensemble for control.

2000 Mathematics Subject Classification: 17B37; 05E15

Thesis (Ph. D.)--University of Oregon, 2007. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 209-231). Also available for download via the World Wide Web; free to University of Oregon users.

Thesis (Ph. D.)--University of Nevada, Reno, 2007. / "August, 2007." Includes bibliographical references (leaves 150-154). Online version available on the World Wide Web.