Quantum mechanics of topological solitons

Topological solitons - are of broad interest in physics. They are objects with localised energy and stability ensured by their topological properties. It is possible to create them during phase transitions which break some sym- metry in a frustrated system. They are ubiquitous in condensed matter, ranging from monopole excitations in spin ices to vortices in superconduc- tors. In such situations, their behaviour has been extensively studied. Less well understood and yet equally interesting are the symmetry-breaking phase transitions that could produce topological defects is the early universe. Grand unified theories generically admit the creation of cosmic strings and monopoles, amongst other objects. There is no reason to expect that the behaviour of such objects should be classical or, indeed, supersymmetric, so to fully understand the behaviour of these theories it is necessary to study the quantum properties of the associated topological defects. Unfortunately, the standard analytical tools for studying quantum field theory - including perturbation theory - do not work so well when applied to topological defects. Motivated by this realisation, this thesis presents numerical techniques for the study of topological solitons in quantum field theory. Calculations are carried out nonperturbatively within the framework of lattice Monte Carlo simulations. Methods are demonstrated which use correlation functions to study the mass, interaction form factors, dispersion relations and excitations of quantum topological solitons. Results are compared to exact expressions obtained from integrability, and to previous work using less sophisticated numerical techniques. The techniques developed are applied to the prototypical kink soliton and to the 't Hooft-Polyakov monopole

On the quantum stability of Q-balls

We consider the evolution and decay of Q-balls under the influence of quantum fluctuations. We argue that the most important effect resulting from these fluctuations is the modification of the effective potential in which the Q-ball evolves. This is in addition to spontaneous decay into elementary particle excitations and fission into smaller Q-balls previously considered in the literature, which -- like most tunnelling processes -- are likely to be strongly suppressed. We illustrate the effect of quantum fluctuations in a particular model $\phi^6$ potential, for which we implement the inhomogeneous Hartree approximation to quantum dynamics and solve for the evolution of Q-balls in 3+1 dimensions. We find that the stability range as a function of (field space) angular velocity $\omega$ is modified significantly compared to the classical case, so that small-$\omega$ Q-balls are less stable than in the classical limit, and large-$\omega$ Q-balls are more stable. This can be understood qualitatively in a simple way.Comment: JHEP format, 17+1 pages, 9 figures; v2: improvements to several figures, text rewritten to improve legibility, conclusions unchanged, published in JHE

Widowhood, Divorce, and Loss of Health Insurance Among Near Elderly Women: Evidence from the Health and Retirement Study

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Gravitational waves from a first-order electroweak phase transition : a brief review

We review the production of gravitational waves by an electroweak first-order phase transition. The resulting signal is a good candidate for detection at next-generation gravitational wave detectors, such as LISA. Detection of such a source of gravitational waves could yield information about physics beyond the Standard Model that is complementary to that accessible to current and near-future collider experiments. We summarize efforts to simulate and model the phase transition and the resulting production of gravitational waves. This article is part of the Theo Murphy meeting issue 'Higgs cosmology'.Peer reviewe

Acoustic waves and the detectability of first-order phase transitions by eLISA

In various extensions of the Standard Model it is possible that the electroweak phase transition was first order. This would have been a violent process, involving the formation of bubbles and associated shock waves. Not only would the collision of these bubbles and shock waves be a detectable source of gravitational waves, but persistent acoustic waves could enhance the signal and improve prospects of detection by eLISA. I summarise the results of a recent campaign to model such a phase transition based on large-scale hydrodynamical simulations, and its implications for the eLISA mission.Peer reviewe

Studying a relativistic field theory at finite chemical potential with the density matrix renormalization group

The density matrix renormalization group is applied to a relativistic complex scalar field at finite chemical potential. The two-point function and various bulk quantities are studied. It is seen that bulk quantities do not change with the chemical potential until it is larger than the minimum excitation energy. The technical limitations of the density matrix renormalization group for treating bosons in relativistic field theories are discussed. Applications to other relativistic models and to nontopological solitons are also suggested.Comment: 9 pages, 5 figures; v2: title changed; references added, conclusions expanded, to be published in PR

The Economic Consequences of Widowhood

We analyzed the economic consequences of a husband’s death using events that occurred between the first two waves of the HRS and AHEAD studies. We compared poverty transitions against published results from Social Security’s Retirement History Survey of the 1970s. Widowhood remains an important risk factor for transition into poverty, although somewhat less so than twenty years ago. Women over age 65 (AHEAD) are less likely to experience severe economic changes than women under age 61 (HRS). Several factors account for the age differences: the declining importance of husband’s earnings with age, the rising importance of Social Security benefits, and the occasionally large out-of-pocket medical expenses associated with husband’s death before Medicare eligibility. The greater economic impact of widowhood at younger ages is consistent with our cross-section evidence that poverty rates rise with duration of widowhood but are only weakly associated with age.