This thesis is devoted to studying two important aspects of braneworld physics: their cosmology and their holography. We examine the Einstein equations induced on a general (n - 2)-brane of arbitrary tension, embedded in some n-dimensional bulk. The brane energy-momentum tensor enters these equations both linearly and quadratically. From the point of view of a homogeneous and isotropic brane we see quadratic deviations from the FRW equations of the standard cosmology. There is also a contribution from a bulk Weyl tensor. We study this in detail when the bulk is AdS-Schwarzschild or Reissner-Nordstrom AdS. This contribution can be understood holographically. For the AdS-Schwarzschild case, we show that the geometry on a brane near the AdS boundary is just that of a radiation dominated FRW universe. The radiation comes from a field theory that is dual to the AdS bulk. We also develop a new approach which allows us to consider branes that are not near the AdS boundary. This time the dual field theory contributes quadratic energy density/pressure terms to the FRW equations. Remarkably, these take exactly the same form as for additional matter placed on the brane by hand, with no bulk Weyl tensor. We also derive the general equations of motion for a braneworld containing a domain wall. For the critical brane, the induced geometry is identical to that of a vacuum domain wall in (n-l)-dimensional Einstein gravity. We develop the tools to construct a nested Randall-Sundrum scenario whereby we have a "critical" domain wall living on an anti-de Sitter brane. We also show how to construct instantons on the brane, and calculate the probability of false vacuum decay.

by Poon Kai Lok. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (p. 128-130). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese. / by Poon Kai Lok.

Li, Xiaoke = 超冷旋量混合物中的異核間相干自旋動力學 / 李小科. / Thesis Ph.D. Chinese University of Hong Kong 2015. / Includes bibliographical references (leaves 126-142). / Abstracts also in Chinese. / Title from PDF title page (viewed on 25, October, 2016). / Li, Xiaoke = Chao leng xuan liang hun he wu zhong de yi he jian xiang gan zi xuan dong li xue / Li Xiaoke.

In this thesis we develop a fully quantum-mechanical treatment of collisions between distinct atomic Bose-Einstein condensate wavepackets, with particular emphasis on the incoherently scattered atoms that form s-wave haloes around the condensate wavepackets. Previous theoretical treatments of these systems have been unable to account simultaneously for both the evolution of the halo and the depletion of the condensates, and were therefore restricted to the small scattering limit. Our approach uses the truncated Wigner method, a particular example of the classical field methods familiar from quantum optics. The atomic field is restricted to a low-energy subspace of single-particle states, and the method is applicable even to highly-scattered systems. We present a comprehensive derivation of the truncated Wigner method for ultracold bosonic fields, and discuss in detail the validity regime of the Wigner truncation for inhomogeneous multimode systems. The method gives rise to a set of coupled stochastic differential equations that describe the evolution of a single realisation of the atomic field, and have a form similar to that of the well known Gross-Pitaevskii equation, but with the important difference that the stochastic differential equations include well prescribed quantum fluctuations. To propagate our systems we develop algorithms that allow for highly efficient numerical evolution of realistic experimental collisions. By investigating individual trajectories of the colliding system, we find that the scattering halo is composed of many distinct highly-populated phase grains separated by large numbers of vortices, a behaviour we label quantum turbulence. We develop a spatial averaging method for approximately calculating quantum correlation functions from a single trajectory, and calculate various properties of the halo. Based on these results, we propose a mechanism to explain the observed features of scattering halo formation. We find by using an appropriately extended truncated Wigner approach that three-body recombination events have negligible effect on the collisions. Using an ensemble of trajectories we calculate correlation functions of a particular collisional system to give a rigorous characterisation of the quantum statistics of the field, and obtain results that are remarkably similar to those obtained using single trajectory spatial averaging. For global field quantities, such as the total coherent population, we find that accurate estimates can be achieved using just two trajectories, a result we use to efficiently explore the dependence of the system on key physical parameters. Finally, we apply the truncated Wigner method to collisions between condensates in differing hyperfine states, whose (single-trajectory and ensemble) behaviour we find is qualitatively similar to that of single-component collisions.

The mesoscopic effects in the quantum trapped gases of the Bose atoms constitute the main subject of the present thesis. These effects are the most difficult for the theoretical analysis in the quantum statistical physics since they can’t be seen by neither a standard quantum mechanics of the simple microscopic systems of one or very few atoms nor a standard statistical physics of the macroscopic systems that are infinite in the bulk (thermodynamic) limit. Most of the experiments on the cold quantum gases performed in the last decade, starting from the first demonstration of BEC in 1995, involve the mesoscopic systems of a finite number of atoms. The mesoscopic effects should manifest themselves most clearly and easily near a critical temperature of BEC; however, they could be observed also above and below the critical temperature. Here I study the quantum and thermal fluctuations of the Bose-Einstein condensate (BEC) in a box with the periodic boundary conditions under a particle-number constraint. The above constraint is the only reason for the BEC and is crucial for the mesoscopic effects in the BEC fluctuations, especially in the vicinity of the critical temperature in the Bose gas. I employ the particle-number conserving operator formalism of Girardeau and Arnowitt introduced in 1959 to analyze the canonical ensemble fluctuations. I present analytical formulas and numerical calculations for the central moments of the ground state occupation fluctuations in an ideal Bose gas in a box with a mesoscopic number of particles. I present the analysis of the BEC statistics both on a temperature at a fixed number of particles and on a number of particles at a fixed temperature. Both analyses are valid for the purpose of understanding the important mesoscopic effects near the critical temperature. I emphasize the non-Gaussian nature of the fluctuations. The presented formalism can be generalized to the case of a weakly interacting Bose gas in a box in the framework of the Bogoliubov approximation. The work in this direction is in progress but is not included in the present thesis.

Diss.--Hamburg Universität, 2000. / Bibliogr. p.169-178.

Thesis (M. Sc.)--University of Queensland, 2002. / Includes bibliographical references.

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: interferometry; bose-einstein condensation. Includes bibliographical references (p. 49-50).

My dissertation is an interdisciplinary work dealing with the intersection of the work of the Cuban poet, essayist, novelist, editor and cultural promoter José Lezama Lima (La Habana, Cuba, 1910-1976) with some of the main Western scientific developments and discoveries of the first half of the twentieth century. Even when a considerable number of canonical studies have mapped Lezama's place in the cartographies of modern and postmodern thought, what I do is completely new in this field. In my work I combine methods and insights from Cuban intellectual history and cultural studies, about the impact of new development in physics and mathematics on the discourse of the humanities and the literary and popular imagination, to do a new type of close reading of Lezama's texts, one that reveals the important role that key elements that he "appropriated" from Riemann geometry, relativity theory, quantum physics, and thermodynamics play in the fashioning of his ambitious "poetic system of the world." Although this type of analysis has successfully been applied to other authors such as James Joyce and Jorge Luis Borges, no attempt has been made to study Lezama Lima’s work from this perspective. I argue that examining the structural and organic relationships of Lezama with the work of scientists such as Albert Einstein provides a unique and effective framework for understanding the "chaos-like" and "fractal-like" theoretical and temporal complexities displayed by the Cuban author in his work. / text

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