Harper型算子的半经典色散关系
On semiclassical dispersion relations of Harper-like operators
摘要：
我们描述了一些半经典谱性质的哈珀类运营商，即一维量子哈密顿周期的动量和位置。在整数通量的情况下，研究了经典Hamilton量的分离面所对应的谱区域。我们推导出色散关系的渐近公式，带隙的宽度，并显示几何特性和不对称的哈密顿量的影响的能带的形式。
英文摘要：
We describe some semiclassical spectral properties of Harper-like operators, i.e. of one-dimensional quantum Hamiltonians periodic in both momentum and position. The spectral region corresponding to the separatrices of the classical Hamiltonian is studied for the case of integer flux. We derive asymptotic formula for the dispersion relations, the width of bands and gaps, and show how geometric characteristics and the absence of symmetries of the Hamiltonian influence the form of the energy bands.
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