Yi wei chao leng yuan zi xi tong zhong de duo ti wu li

In the first part of the thesis, we investigate ground state properties of Tonks-Girardeau(TG) gas in an one-dimensional periodic trap. The key issue we are interested in is whether periodically-trapped TG gas has an off-diagonal long range order. Through numerical calculations, the single-particle reduced density matrix is computed for systems with up to 265 bosons. Scaling analysis on the occupation number of the lowest orbital shows that there is no Bose-Einstein condensation for the periodically-trapped TG gas in both commensurate and incommensurate cases. We find that, for the commensurate case, the scaling exponents of the occupation number of the lowest orbital, the amplitude of the lowest orbital and the zero-momentum peak height with the particle numbers are 0, 0.5 and 1, respectively, while for the incommensurate case, they are 0.5, 0.5, and 1.5, respectively. These exponents are related to each other by a universal relation.In the second part we study the one-dimensional "hard-sphere" fermions and bosons systems. The pair distribution functions of the one-dimensional "hard-sphere" fermions and bosons systems have been exactly evaluated by introducing gap variables. Some interesting results are obtained. Meanwhile, the pair distribution function could be measured in experiments, so hopefully our numerical results may be observed experimentally in the near future.Lastly, we investigate the one-dimensional multi-component fermions and bosons systems. This is an extension of the work of C.N.Yang and Y.Z.You in 2011. Yang and You studied the ground state energy of w-component fermions and bosons with repulsive interactions. In this part, we investigate w-component fermions and bosons in an attractive interaction regime. Several theorems about the ground state energy of w-component fermions and bosons systems are stated and proved. Combing the results in the work of Yang and You, we finally have a comprehensive picture for the ground state energy of one-dimensional fermions and bosons systems. iiiOver the last ten years or so, there have been a number of dramatic experimental developments in trapping, cooling and controlling atoms, which open up new opportunities for studying strongly interacting many-body systems. Cold atom systems are very clean and highly tunable. Systems with different dimensionalities can be realized through optical lattice confinement, and the interactions between atoms can be fine-tuned to any value desired by Feshbach resonance. In this way various simple models can be realized to analyze subtle many-body problems which are difficult to analyze because of the complexity of the systems in real materials.Wei, Bobo = 一維超冷原子系統中的多體物理 / 魏勃勃.Adviser: Hai Qing Lin.Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: .Thesis (Ph.D.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (leaves 76-[80]).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, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.Abstract also in Chinese.Wei, Bobo = Yi wei chao leng yuan zi xi tong zhong de duo ti wu li / Wei Bobo