SU(3) Quantum Spin Ladders as a Regularization of the CP(2) Model at Non-Zero Density: From Classical to Quantum Simulation

Quantum simulations would be highly desirable in order to investigate the finite density physics of QCD. $(1+1)$-d $\mathbb{C}P(N-1)$ quantum field theories are toy models that share many important features of QCD: they are asymptotically free, have a non-perturbatively generated massgap, as well as $\theta$-vacua. $SU(N)$ quantum spin ladders provide an unconventional regularization of $\mathbb{C}P(N-1)$ models that is well-suited for quantum simulation with ultracold alkaline-earth atoms in an optical lattice. In order to validate future quantum simulation experiments of $\mathbb{C}P(2)$ models at finite density, here we use quantum Monte Carlo simulations on classical computers to investigate $SU(3)$ quantum spin ladders at non-zero chemical potential. This reveals a rich phase structure, with single- or double-species Bose-Einstein "condensates", with or without ferromagnetic order

Charmonium Potentials at Finite Temperature

The charmonium states at non-zero temperature are studied on anisotropic lattices with 2 dynamical quark flavours. Non-local operators are used to determine the Nambu-Bethe-Salpeter (NBS) wavefunctions via both conventional fitting methods and the Maximum Entropy Method. The interquark potential is determined from the solution of the Schrodinger equation, given the NBS wavefunction as input following the HAL QCD method. We observe a temperature dependent potential which becomes steeper as the temperature decreases

Non-zero temperature charmonium potentials from the lattice.

A reliable calculation of the charmonium potential at non-zero temperature from first principles is required as part of a wider effort to understand the phase transition of hadronic matter to quark-gluon plasma at high temperature. The interquark potential inside hot matter produced in heavy ion collisions can not be measured directly. Therefore the precise role of the intcrquark potential in quark-gluon plasma formation can currently only be determined through a reliable theoretical calculation. In this thesis charmonium potentials are obtained from dynamical lattice simulations of quantum chromodynamics by analysing correlators using two different approaches; i) conventional fitting - correlators are fitted in the conventional manner familiar from hadron spectroscopy on the lattice; ii) the HAL QCD time-dependent method - a novel technique borrowed from nuclear physics is used to derive an expression for the potential directly in terms of the correlators. Recent lattice QCD studies relevant to the charmonium potential fall into two categories: i) non-zero temperature studies of the static quark potential; ii) zero temperature studios with i)hysical charm masses. The results presented in this thesis are novel because they are from a study of the charnionium potential using physical charm masses at non-zero temperature. The charmonium potential obtained from conventional fitting is found to be temperature dependent, as the temperature increases, the potential flattens. However the method suffers from certain reliability issues. The time-dependent method is found to be more suitable than conventional fitting for studying the interquark potential at high temperature. Using the time-dependent method the charmonium potential between 0.76Tc and 1.09Tc is found to be temperature dependent. The result is reliable and shows the potential flattening as the temperature increases, which is consistent with the expectation that at high temperature the interquark potential becomes colour-Debye screened. Extracting the potential from temperatures higher than 1.09Tc would have led to unreliable results, but this limit is specific to the configurations used and not the method itself. The study shows that if configurations are generated with the time-dependent method in mind, then it can be used to extract the charmonium potential at temperatures higher than 1.09Tc

Welfare versus punishment?: The careers of young offenders with a background in public care.

Young people with a background in public care are over-represented in the criminal justice system. The subject of the thesis concerns the relationship between these two systems. The main focus of this qualitative piece of research is an analysis of the cases of thirty young people who have had experience of both systems. Conducted on the site of a Welsh Social Services Youth Justice Team that - during the course of the fieldwork - was reconfigured as a Youth Offending Team, the research was guided by three related questions. Firstly, what was the nature of the relationship between the public care system and the criminal justice system? Secondly, how did such discourses as 'welfare' and 'punishment' influence what happened to young people with care backgrounds in the youth justice system? Thirdly, how did the youth justice reforms of the 1997-2001 Labour government impact on practice at ground level? These questions were addressed by a combination of methods: semi-structured interviews with young people, parents and practitioners; focus groups with professional staff; observation; and analysis of case files and other agency documents. The analysis identified a number of social and institutional processes that criminalised children in public care and accelerated their 'progress' through the criminal justice system