【作者】 吴大鹏；

【导师】 门福殿；

【作者基本信息】 中国石油大学 ， 理论物理， 2008， 硕士

【摘要】 玻色-爱因斯坦凝聚(BEC)是近年来物理学界的研究热点之一.它揭示了一类新的物质状态,高度密集的大量原子以相干的方式演变,将微观的量子现象带到了宏观尺度.激子BEC是在半导体材料中实现的低维玻色-爱因斯坦凝聚,和原子BEC相比,有着更为广阔的前景:如最有希望在大功率、低功耗发光器件和可能在超快逻辑器件及量子计算中得到应用,因而越来越受到人们的重视.凝聚温度是普通玻色气体转变为玻色-爱因斯坦凝聚体的相变温度.本文考虑体系中粒子第一激发态能量不为零的条件下,对低维体系的凝聚温度进行相关计算,考查体系中粒子的第一激发态能量的大小对体系的凝聚温度的影响;以及在第一激发态能量大小一定的前提下,不同维度的空间中体系的凝聚温度、基态占据数随总粒子数变化的关系,得到了与实验较为符合的结果.研究发现:随着粒子数密度的增加,低维体系的凝聚温度比高维情形增长的快;体系的凝聚温度与第一激发态能量密切相关,解释了对于囚禁在GaAs量子阱中的激子气体,即使在无谐振势或幂指数等特殊外势的条件下,也可以在几个K实现玻色-爱因斯坦凝聚的实验现象.玻色-爱因斯坦凝聚体波函数藉由Gross-Pitaevskii方程(G-P方程)描述.最后,我们使用傅立叶-格雷德-哈密顿方法数值求解G-P方程,研究了总粒子数、粒子间相互作用、谐振频率和一般幂指数外势对玻色凝聚体粒子数密度分布、基态能量的影响.研究结果表明:增大幂指数外势、谐振频率,降低粒子间的排斥作用都会增加凝聚体中心的粒子数密度、缩小凝聚体半径;而增大总粒子数、谐振频率、粒子间的排斥作用及幂指数外势的指数都会增大体系的基态能量;随着总粒子数增大,数值结果与托马斯-费米近似结果渐趋一致,托马斯-费米近似在大粒子数条件下是一种较好的近似方法,在粒子数有限时,托马斯-费米结果与真实情形偏差较大,应采用数值解法.更多还原

【Abstract】 Bose-Einstein Condensation (BEC) is one of the hotspot in the physics research recently. It reveals a new form of matter in the universe, a large number of dense atoms evolves coherently, bringing the quantum phenomenon from the microscopic world to the macroscopic world. Excitons BEC is the Bose-Einstein Condensation realized in the semi-conductor materials. The physists lay more and more emphasis on it due to it’s speciality and wide prospect, such as the application on high-powered and low-consumption light-emitting devices, ultra-fast logic devices, and quantum computing. Critical temperature is the phase transition temperature at which the common bose gas transforms into the Bose-Einstein Condensation. This thesis calculates the critical temperature in the low dimensional spaces according to the first-excited-state energy of particles in the traped condensate being different from zero, investigates the effect of first-excited-state energy on the critical temperature as well as the relationship of the critical temperature and the ground-state faction versus the total number of particles in different dimensional spaces. The results we get are consistent with the experiment data. It is shown that the critical temperature in low-dimensional spaces increases more quickly than that in high-dimensional space with density of particle number increasing, and the critical temperature of system has close relation to the first-excited-state energy. Our theoretical method can explain the phenomena that even under the condition of absent special external potential, such as harmonic potential and power-law potential, the Bose-Einstein Condensation can be realized at several K for excitons gas trapped in GaAs quantum well. The wave function of BEC can be described by the Gross-Pitaevskii equation. In the last part of the thesis, we study the effect of total particle number, the interaction between particles, the frequency of harmonic potential and the power-law potential on the distribution of the particles in BEC and the ground state energy of the condensate by solving the G-P equation using the Fourier-Grid-Hamiltonian method numerically. The results we get show that with the intensity of power-law potential or the frequency of harmonic potential increases or the repulsive interaction between particles decreases, the particle density in the condensate center will increase and the radius of the condensate will decrease. The ground state energy of the BEC will rise with the increase of the total particle number, the repulsive interaction between particles, the frequency of harmonic potential and the intensity of power-law potential. Thomas-Fermi approximation grows more and more resembling with the numeric result when the particle number increases, which shows Thomas-Fermi limit is a good method in the condition of large particle number, if the particle number in the system is less, the numeric way should be use when study the BEC problem.更多还原