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Ng Ho Tsang = 玻色-愛因斯坦凝聚態在一個雙井形位勢的量子糾纏的理論 / 吳浩錚. / "1st November 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 159-167) / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese. / Ng Ho Tsang = Bose-Aiyinsitan ning ju tai zai yi ge shuang jing xing wei shi de liang zi jiu chan de li lun / Wu Haozheng.

In this thesis we develop Bragg scattering as a tool for probing and manipulating ultra-cold atoms. Our approach is based on a mean-field treatment of degenerate quantum gases. Bose-Einstein condensates are described by the Gross-Pitaevskii equation and degenerate Fermi gases are described by the Bogoliubov-de-Gennes equations. Our work is presented in three inter-related topics. In Part I we investigate Bose-Einstein condensation in a time-averaged orbiting potential trap by deriving solitary-wave dynamical eigenstates of the system. We invoke the quadratic average approximation in which the dynamic effects of the time-dependent potential can be described simply, even when accounting for atomic collisions. By deriving the transformation to the translating frame, dynamical eigenstates of the system are defined and those states are solitary-wave solutions in the laboratory frame, with a particular circular centre-of-mass motion independent of the strength of the collisional interactions. Our treatment in the translating frame is more general than previous treatments that use the rotating frame to define system eigenstates, as the use of the rotating frame restricts eigenstates to those that are cylindrically symmetric about their centre of mass. In Part II we describe Bragg spectroscopy of a condensate with solitary-wave motion. Our approach is based on a momentum space two-bin approximation, derived by Blakie et al. [Journal of Physics B 33:3961, 2000] to describe Bragg scattering of a stationary condensate. To provide an analytic treatment of Bragg scattering of a solitary-wave condensate we use the translating frame, in which the time dependence of the system is described entirely by a time-dependent optical potential. We derive a simplified treatment of the two-bin approximation that provides a physical interpretation of the Bragg spectrum of a solitary-wave condensate. Our methods are applied to Bragg spectroscopy of a condensate in a time-averaged orbiting potential trap, which accelerates as a solitary wave as derived in Part I. The time-averaged orbiting potential trap system is ideal for testing our approximate analytic methods because the micromotion velocity is large compared to the condensate momentum width. In Part III we present a theoretical treatment of Bragg scattering of an ultra-cold Fermi gas. We give the first non-perturbative numerical calculations of the dynamic behaviour of a degenerate Fermi gas subjected to an optical Bragg grating. We observe first order Bragg scattering, familiar from Bragg scattering of stationary Bose-Einstein condensates, and at lower Bragg frequencies we predict scattering of Cooper pairs into a correlated spherical shell of atoms. Correlated-pair scattering is associated with formation of a grating in the pair potential. We give an analytic treatment of Bragg scattering of a homogeneous Fermi gas, and develop a model that reproduces the key features of the correlated-pair Bragg scattering. We discuss the effect of either a trapping potential or finite temperature on the correlated-pair Bragg scattering.

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references (leaves 126-136). Available also in a digital version from Dissertation Abstracts.

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This thesis deals with Einstein metrics and the Ricci flow on compact mani- folds. We study the second variation of the Einstein-Hilbert functional on Ein- stein metrics. In the first part of the work, we find curvature conditions which ensure the stability of Einstein manifolds with respect to the Einstein-Hilbert functional, i.e. that the second variation of the Einstein-Hilbert functional at the metric is nonpositive in the direction of transverse-traceless tensors. The second part of the work is devoted to the study of the Ricci flow and how its behaviour close to Einstein metrics is influenced by the variational be- haviour of the Einstein-Hilbert functional. We find conditions which imply that Einstein metrics are dynamically stable or unstable with respect to the Ricci flow and we express these conditions in terms of stability properties of the metric with respect to the Einstein-Hilbert functional and properties of the Laplacian spectrum. / Die vorliegende Arbeit beschäftigt sich mit Einsteinmetriken und Ricci-Fluss auf kompakten Mannigfaltigkeiten. Wir studieren die zweite Variation des Einstein- Hilbert Funktionals auf Einsteinmetriken. Im ersten Teil der Arbeit finden wir Krümmungsbedingungen, die die Stabilität von Einsteinmannigfaltigkeiten bezüglich des Einstein-Hilbert Funktionals sicherstellen, d.h. die zweite Varia- tion des Einstein-Hilbert Funktionals ist nichtpositiv in Richtung transversaler spurfreier Tensoren. Der zweite Teil der Arbeit widmet sich dem Studium des Ricci-Flusses und wie dessen Verhalten in der Nähe von Einsteinmetriken durch das Variationsver- halten des Einstein-Hilbert Funktionals beeinflusst wird. Wir finden Bedinun- gen, die dynamische Stabilität oder Instabilität von Einsteinmetriken bezüglich des Ricci-Flusses implizieren und wir drücken diese Bedingungen in Termen der Stabilität der Metrik bezüglich des Einstein-Hilbert Funktionals und Eigen- schaften des Spektrums des Laplaceoperators aus.

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The present thesis is devoted to an analysis of the possibility of Bose condensates supporting persistent currents in the ring geometry. Our analysis is based on an approach developed by F. Bloch which focuses on the ground state energy of the condensate as a function of its angular momentum L. According to this approach, persistent currents are stable if the energy exhibits a local minimum at some nonzero angular momentum. We have used this approach for a single-species gas within a mean- eld approximation to show that persistent currents are stable at integral multiples of N*hbar, where N is the number of atoms in the system, provided a certain interaction parameter exceeds some critical value. These results are extended to a binary mixture of bosonic atoms and we show that the system is still capable of supporting persistent currents under certain conditions. Some of our conclusions contradict those appearing in the earlier literature. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2012-03-27 10:05:21.831