标题： von Neumann格子中的通量态与分数量子霍尔效应 显示英文标题

标题： Flux State in von Neumann lattice and Fractional Hall Effect

摘要： 量子霍尔动力学使用von Neumann格子的中心坐标表述。 给出了霍尔电导率的拓扑不变表达式，并提出了一种基于通量凝聚的新平均场理论来解释分数霍尔效应。 由于我们的平均场哈密顿量与霍夫斯塔特哈密顿量具有相同的形式，因此可以从霍夫斯塔特的谱中理解分数霍尔效应的特征。 计算了能隙和其他物理量，并将其与实验进行了比较。 得到了合理的吻合。 显示英文摘要

摘要： Formulation of quantum Hall dynamics using von Neumann lattice of guiding center coordinates is presented. A topological invariant expression of the Hall conductance is given and a new mean field theory of the fractional Hall effect based on flux condensation is proposed. Because our mean field Hamiltonian has the same form as Hofstadter Hamiltonian, it is possible to understand characteristic features of the fractional Hall effect from Hofstadter's spectrum. Energy gap and other physical quantities are computed and are compared with the experiments. A reasonable agreement is obtained.