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Many-body Dimensional Perturbation Theory for Quantum Confined Systems. Application to Bose-Einstein condensates and quantum nanostructures

Автор:   Brett M.
мягкая обложка
176 страниц
2008 год
Издательство:   Книга по Требованию
Цена:
2781 руб
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Описание:Systems that involve N identical, interacting particles under quantum confinement appear throughout many areas of physics, including chemical, condensed matter, and atomic physics. We use the Wilson FG matrix method to derive general, analytical expressions for the many-body normal-mode vibrational frequencies, and we give analytical results for three N-body quantum-confined systems: the N-electron atom, N-electron quantum dot, and N-atom inhomogeneous Bose-Einstein condensate with a repulsive hard-core potential. In this thesis, we present the methods of dimensional perturbation theory, a powerful set of tools that uses symmetry to yield simple results for studying such many-body systems. We present a detailed discussion of the dimensional continuation of the N-particle Schrodinger equation, the D? ? equilibrium structure, and the normal-mode oscillations of this structure.


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The Grand Design

The laws of M-theory therefore allow for different universes with different apparent laws, depending on how the internal space is curled. M-theory has solutions that allow for many different internal spaces, perhaps as many as 10500, which means it allows for 10500 different universes, each with its own laws. To get an idea how many that is, think about this: If some being could analyze the laws predicted for each of those universes in just one millisecond and had started working on it at the big bang, at present that being would have studied just 1020 of them. And thatБЂ™s without coffee breaks. Centuries ago Newton showed that mathematical equations could provide a startlingly accurate description of the way objects interact, both on earth and in the heavens. Scientists were led to believe that the future of the entire universe could be laid out if only we knew the proper theory and had enough computing power. Then came quantum uncertainty, curved space, quarks, strings, and extra dimensions, and the net result of their labor is 10500 universes, each with different laws, only one of which corresponds to the universe as we know it ...»

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