波-爱凝结研究中若干前沿问题的理论探索

In this study it was pointed out that the functional integral approach in quantum statistics (FIA) is not only a method, but also can be its third formulation. A. It covers the field of statistical mechanics; B. It has sound mathematical bases; C. Our theory in two points improved the Hubbard theory: 1. The dimensionality of the infinite dimensional integrals was reduced in principle; 2. There is no need for the infinite dimensional canonicaltransformation, which is necessary and difficult in Hubbard theory. D. We have solved the famous divergence (mathematical break down) problem in the functional integral approach of Anderson model. E. A possible investigation on phase transition by this formulation has been made. It further suggests us to study the exact solution of Bose-Einstein condensation (BEC) by FIA. We also proposed an exactly soluble model, obtained its exact solution and BEC distribution for an interacting system. Its shifts of Tc by interaction were studied. This is a hot field fighting by some PRL papers. Based on our exact solution, under a trustable approximation, our result will be exact the same as that of Kerson Huang in PRL This set a sound foundation for further studies on the third formulation in quantum statistics. Besides,the thermodynamic properties, distributions of ideal Bose gases in harmonic traps were studied analytically and numerically. Detailed investigation of the BEC stabilities of attractive Bose system in anisotropic traps, their instability boundaries by Bogoliubov transformation and the corresponding problems in low dimensions have been made. This project also made a series and "highly original studies" on the inverse problems of emissivity etc. The three rapid communications in PRE were highly appreciated by referees. Then they formed a new project supported by NSFC.

发展适合非均匀玻色体系的量子统计中泛函积分理论,越出平均场理论近似.进而发展其泛函积分理论的严格可解模型.研究越出博格柳玻夫近似的理论和方法,在元激发谱的国际争论和泛函积分理论研究BEC的领域中取得领先结果和地位.建议一个基于BEC的高温超导模型,用反演理论研究约束几何下液氨gama线后移及建议与BEC有关的效应和应用等.