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In this thesis, particle- particle angular correlations for reactions in non-zero degree geometry and with non-zero spin nuclei are performed and found to be a valuable tool for spin determination, (d-α) angular correlations in the reaction process ¹⁴N(⁶Li,d)¹⁸F* (α)¹⁴N are measured for three high excited states in ¹⁸F with a ⁶Li beam of 36MeV. Spins and parities for two of the observed states are determined, and in agreement with theoretical predictions, these states are suggested as members of the K^π=1⁺ α-rotational band. The three analysed 9.58MeV 6⁺, 11.2MeV, 14.1MeV 8⁺ states are found to undergo a predominant α-particle decay to the ground state of ¹⁴N. Gamow unbound formalism is carried out for the state descriptions. Angular distributions are measured and analysed under Hauser Feshbach and exact finite range DWBA formalisms. Spectroscopic factors are extracted and compared to shell model predictions, showing a reasonable agreement. (³He-α) and (t-α) angular correlations for the reaction processes ¹⁴N(⁶Li,³He)¹⁷0* (α)¹³C and ¹⁴N(⁶Li,t)¹⁷F* (α)¹³N respectively are measured at 36MeV of ⁶Li. High selectivity is observed for the three particle transfer processes and percentages of the different particle decays for the high populated states are presented. Structureless angular correlations hinder definite spin and parity assignements, but the displacement of the preferred direction observed in the pattern decay gives some information on the range of plausible angular momenta. Shell model calculations are performed for comparison with the experimental data, and this allows tentative spin identifications. EFR EWEA calculations are carried out, providing some confirmation on the spin suggestions. Useful nuclear structure information is obtained for the mass 17 and 18 nuclear states. The particle-particle angular correlation expression for a process where a direct reaction mechanism is involved is reviewed, programmed and used for obtaining the theoretical predictions to be compared to the experimental results.

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More than a century ago, starting with Michelson, the field of classical coherence has developed rapidly. By studying and uncovering the coherence properties of light, many useful applications were discovered. In modern times, these applications have seen large use in fields like astronomy, where the properties of light can be used to discover stars and determine their radius, for example. Another class of correlations, namely quantum correlations, which were discovered in the beginning of the twentieth century, have gained much attention from the scientific community in the last two decades. In particular, the field of quantum information developed, promising great computational power by using quantum correlations to build computers. Currently, quantum computation is a very active field bringing together physicists, mathematicians, engineers, chemists, and computer scientists to find solutions to the problems encountered in building quantum computers. I consider some classical coherence effects of the degree of cross polarization (DCP) on the Hanbury-Brown Twiss effect, with a specific focus on Gaussian Schell-model beams. I show that the DCP is necessary, in general, to determine the correlations in intensity fluctuations of a beam at two different points. As for quantum correlations, I consider entanglement in realistic systems: one in two-qubit systems, and the other in continuous variable quantum systems. In the former case, when the temperature of the system is finite, entanglement always decays in a finite time. However, in the latter case, entanglement is long-lived, although in the long run it is not of much practical use. Finally, I unravel the relationship between quantum discord and quantum entanglement, as well as quantum discord and entropy for the most general two-qubit systems, and I identify the states that define the boundaries of these relationships.

More than a century ago, starting with Michelson, the field of classical coherence has developed rapidly. By studying and uncovering the coherence properties of light, many useful applications were discovered. In modern times, these applications have seen large use in fields like astronomy, where the properties of light can be used to discover stars and determine their radius, for example. Another class of correlations, namely quantum correlations, which were discovered in the beginning of the twentieth century, have gained much attention from the scientific community in the last two decades. In particular, the field of quantum information developed, promising great computational power by using quantum correlations to build computers. Currently, quantum computation is a very active field bringing together physicists, mathematicians, engineers, chemists, and computer scientists to find solutions to the problems encountered in building quantum computers. I consider some classical coherence effects of the degree of cross polarization (DCP) on the Hanbury-Brown Twiss effect, with a specific focus on Gaussian Schell-model beams. I show that the DCP is necessary, in general, to determine the correlations in intensity fluctuations of a beam at two different points. As for quantum correlations, I consider entanglement in realistic systems: one in two-qubit systems, and the other in continuous variable quantum systems. In the former case, when the temperature of the system is finite, entanglement always decays in a finite time. However, in the latter case, entanglement is long-lived, although in the long run it is not of much practical use. Finally, I unravel the relationship between quantum discord and quantum entanglement, as well as quantum discord and entropy for the most general two-qubit systems, and I identify the states that define the boundaries of these relationships.

This thesis studies three topics in quantum computation and information: The approximability of quantum problems, quantum proof systems, and non-classical correlations in quantum systems. Our first area of study concerns the approximability of computational problems which are complete for quantum complexity classes. In the classical setting, the study of approximation algorithms and hardness of approximation is one of the main research areas of theoretical computer science. Yet, little is known regarding approximability in the quantum setting. We first demonstrate a polynomial-time approximation algorithm for dense instances of the canonical QMA-complete quantum constraint satisfaction problem, the local Hamiltonian problem. We next go in the opposite direction by first introducing a quantum generalization of the polynomial-time hierarchy. We then introduce problems which are not only complete for the second level of this hierarchy, but are in fact hard to approximate. Our second area of study concerns quantum proof systems. Here, an interesting question which remains open despite much effort is whether a proof system with multiple unentangled quantum provers is equal in expressive power to a proof system with a single quantum prover (i.e. is QMA(poly) equal to QMA?). Our results here study variants of this question, and include a proof that the class BellQMA(poly) collapses to QMA. We also give an alternate proof that SepQMA(m) admits perfect parallel repetition. This proof is novel in that it utilizes cone programming duality. Our final area of study concerns non-classical correlations in quantum systems. Specifically, there exist genuinely quantum correlations beyond entanglement in mixed quantum states which may prove useful from a computing and information theoretic perspective. We first explore the presence of such correlations in the locking of classical correlations and the DQC1 model of mixed-state quantum computing. Our second result introduces a novel scheme for quantifying non-classical correlations using local unitary operations. Our third result introduces a protocol through which non-classical correlations in a starting system can be “activated”' into distillable entanglement with an ancilla system. Our last result determines when the entanglement generated in the activation protocol above can be mapped back onto the starting state via entanglement swapping.

This thesis is directed at exploiting information in the coda of seismic phases and the ambient noise field to provide new constraints on the structure of the Australian Continent. ¶ The exploitation of the immediate coda following the onset of P waves from a distant earthquake using radial receiver functions is now a well established method. The 40 sec interval following P contains reverberations and conversions, by deconvolving the radial component trace with the vertical components, the conversions are emphasized by canceling the part of the response that are common to both components. A member of different styles of such deconvolution, are investigated and a variant of the multitaper method is adopted for subsequent applications. The TASMAL experiment 2003-2005 spans the expected location of the transition between Precambrian and Phanerozoic Australia. The 20 portable broadband stations were exploited in receiver function studies to extract S wave crustal structure through the inversion of stacked receiver functions using the Neighbourhood Algorithm. There is no clear crustal transition associated with the presence of Tasman Line. The Precambrian Cratons tend to exhibit crustal thicknesses close to 40 km but such values are also found in some Phanerozoic sites. ¶ The second part of the thesis is directed at the exploitation of ambient noise or seismic coda to gain information on the Green's function between seismic stations. The TASMAL experiment covered a significant fraction of the Australian continent with a simultaneous deployment of portable broadband stations. From these continuous records, it has proved possible to extract very clear Rayleigh wave signals for station separations up to 2000 km, and to demonstrate the frequency dependent variations in group velocity behaviour. The combination of the paths between the 20 stations localize such behaviour, but detailed images needed more data. The entire archive of portable broadband data recorded by RSES was mined, and combined with data from permanent stations to provide more than 1100 estimates of interstation Green's functions within Australia. Group velocity analysis as function of frequency was followed by nonlinear tomography with the Fast Marching Method. The resulting images of group velocity patterns as a function frequency show pronounced regions of lowered group velocities, most of which match regions of thick sediment. The frequency dependence is not consistent with just sedimentary structure and low midcrustal velocities, most likely due to elevated temperatures, are also needed. ¶ The surface wave portion of the interstation Green's function is the most energetic, and is normally all that seen in ambient noise studies. However, in the coda of events record at the broadband Warramunga seismic array in the Northern Territory, the P and S body wave components also emerge. The characteristics of these arrivals match those observed from nearby small earthquakes. The stacked cross-correlation is the normal approach to enhance Green's function information from ambient noise, but a broader spectral band width with the same phase response can be found by spectral division. It appears advantageous to compare both approaches and select the best result, since very little modifications to procedures are needed. ¶ The properties of the ambient noise at a single station have been investigated in the logarithmic spectral domain and a station dependent signal can be extracted by stacking. The signal appears to be related to the local structure beneath the station, and when fully characterized may provide a new means of investigating structure.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.