In this work, we provide results on the long-time localization in space (dynamical localization) of certain two-dimensional magnetic quantum systems. The underlying Hamiltonian may have the form \(H=H_0+W\), where \(H_0\) is rotationally symmetric and has dense point spectrum and W is a perturbation that breaks the rotational symmetry. In the latter case, we also give estimates for the growth of the angular momentum operator in time.

中文翻译：

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二维磁量子系统的渐近动力学

在这项工作中，我们提供了某些二维磁量子系统在空间中的长期定位（动态定位）的结果。下层的哈密顿量可以具有\（H = H_0 + W \）的形式，其中\（H_0 \）是旋转对称的，并且具有密集的点谱，而W是破坏旋转对称性的扰动。在后一种情况下，我们还估算了角动量算子随时间的增长。