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Interpretation of magneto-oscillatory spectra in cuprous oxide as quantum manifestation of classical non-integrability

机译：氧化亚铜中的磁振荡谱解释为经典不可积性的量子表示

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摘要

The magneto-oscillatory spectra in cuprous oxide (Cu_2O) are observed to have multi-oscillatory structure, and this structure is successfully interpreted as a consequence of classical non-integrability of the Hamiltonian of an electron-hole (e-h) pair generated in the sample in magnetic fields. The spectra are analyzed with the use of the Heller formula which connects absorption cross section with overlap integral of the photon-absorbed wave function (PAWF) as a function of time. The overlap integral in our spectra are experimentally obtained by inverse Fourier transform of the spectra, and three characteristic times are observed as the peak times of the overlap integral. Then, the overlap integral is numerically estimated by calculating recurrence times of the trajectories of a classical hydrogen atom in magnetic fields. The characteristic times and the recurrence times coincide with each other well.
机译：观察到氧化亚铜（Cu_2O）中的磁振荡光谱具有多振荡结构，并且该结构被成功解释为样品中生成的电子-空穴（eh）对的哈密顿量的经典不可积性的结果在磁场中。使用Heller公式对光谱进行分析，该公式将吸收截面与光子吸收波函数（PAWF）的重叠积分作为时间的函数进行连接。我们的光谱中的重叠积分是通过光谱的傅立叶逆变换实验获得的，观察到三个特征时间作为重叠积分的峰值时间。然后，通过计算磁场中经典氢原子的轨迹的递归时间来对重叠积分进行数值估计。特征时间和重复时间很好地重合。

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