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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >Coincidence of quantum-classical orbits for periodically driven two-dimensional anisotropic oscillator-Berry phase and Hannay angle
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Coincidence of quantum-classical orbits for periodically driven two-dimensional anisotropic oscillator-Berry phase and Hannay angle

机译：周期性驱动的二维各向异性振子-贝里相位和汉尼角的量子经典轨道重合

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摘要

In this paper we study quantum-classical correspondence of a periodically driven two-dimensional (2D) anisotropic-oscillator. In terms of the time-dependent canonical transformation the stationary Lissajous orbits are found along with the Hannay's angle. On the other hand, the stationary wave functions are derived analytically with the help of the generalized gauge transformation. The Berry phase in the original gauge is found to be (n + 1/2) times the nonadiabatic Hannay's angle with the integer number n being the eigenstate index. By using the SU(2) coherent superposition of degenerate 2D-eigenstates for a fixed energy we construct the stationary wave function, the probability cloud of which is shown to coincide perfectly with the classical orbits.
机译：在本文中，我们研究了周期性驱动的二维（2D）各向异性振荡器的量子经典关系。根据与时间有关的典范变换，静止的李沙育轨道与汉尼角一起被发现。另一方面，借助广义规范变换，可以解析得出驻波函数。发现原始量规中的贝里相为非绝热汉尼角的（n + 1/2）倍，整数n为本征态指数。通过使用简并2D本征态的SU（2）相干叠加来获得固定能量，我们构建了平稳波函数，该函数的概率云被证明与经典轨道完全一致。

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