单体和多体量子系统几何相位的研究

【作者】 宋元军；

【导师】 王顺金；

【作者基本信息】 四川大学 ， 理论物理， 2005， 硕士

【摘要】 本文研究复合系统的几何相位存在的两个有待深入探讨的问题:系统的哈密顿量的结构怎样影响几何相位,多粒子系统的几何相位的复杂性如何去描述。主要结果如下:1。运用代数动力学,求解了旋转磁场中的朗道系统的几何相位。数值研究结果显示,绝热几何相位与非绝热几何相位有重大区别:非绝热演化中额外的非绝热量子激发引起系统几何相位的非周期性和复杂性,体现了环境对系统的影响。这一结果,有助于澄清人们对绝热几何相位和非绝热几何相位的关系的认识。2。对三粒子海森堡自旋链多体系统的几何相位的研究结果表明,该系统的哈密顿量的对称性要影响系统的几何相位的演化,当系统哈密顿量的对称性破缺时,几何相位会发生明显变化。系统的几何相位对哈密顿量对称性的这种依赖性,意味着,在用自旋链制成相位门时,应当充分考虑和利用系统的哈密顿量的对称性破缺对几何相位的影响。3。探讨了多粒子系统的几何相位中的分形现象,建立了几何相位与分形的联系,并计算了分形曲线的盒子维数,从而,在理论上拓展了人们对几何相位的认识。更多还原

【Abstract】 This thesis concentrates on the issues of the geometric phase of composite system: the dependence of geometric phase on the coupling between the two subsystems, the effect of the entanglement among particles on the geometric phase of the composite system, the influence of symmetry of Hamilton of composite system on the geometric phase, and the complexity of geometric phase of multi-particle system. Using algebraic dynamics, the geometric phase of Landau system with a rotating magnetic field is studied numerically, and the great difference between adiabatic geometric phase and non-adiabatic geometric phase is shown: in non-adiabatic evolution, non-adiabatic quantum effect results in the non-periodicity and the complexity of geometric phase, which reflected the influence of environment on the system. The investigation of the geometric phase of a 3 spin-1/2 chain shows that the symmetry of Hamilton affects the structure of geometric phase: when the symmetry of Hamilton is broken, a drastic change in the structure of the geometric phase takes place. The fractal phenomenon of geometric phase in an entangled multi-particle system is also explored, and the box-counting dimensions of the fractal-like curves of the evolution of geometric phases are calculated. The results of the thesis are helpful to extend the understanding of geometric phase.更多还原