囚禁离子晶体的简正模、转动惯量和热涨落
Normal Modes, Rotational Inertia, and Thermal Fluctuations of Trapped Ion Crystals
摘要：
基于系统动力学矩阵的厄米特性质，导出了囚禁离子晶体的简正模。这种方法等价于标准的Bogoliubov方法，但对于经典系统，它可以说是更简单和更通用的，因为不需要正则坐标。该理论适用于稳定、不稳定和中性稳定系统。然后将该方法应用于潘宁阱中的离子晶体。大的应用磁场的情况下，减少本征值问题的开发，其中频谱分解成ExB漂移模式，轴向模式，和回旋模式。在这些模式中的热波动水平进行了分析，并示出与玻尔-范-Leeuwen定理是一致的，只要中性稳定的模式与晶体旋转包括在分析中。推导出晶体的转动惯量的表达式，并描述了在大磁场中占主导地位的对该惯量的磁贡献。一个不寻常的限制被发现的特殊情况下，球对称的约束，其中的转动惯量不存在和角动量的变化离开旋转频率不受影响。
英文摘要：
The normal modes of a trapped ion crystal are derived using an approach based on the Hermitian properties of the systems dynamical matrix. This method is equivalent to the standard Bogoliubov method, but for classical systems it is arguably simpler and more general in that canonical coordinates are not necessary. The theory is developed for stable, unstable, and neutrally-stable systems. The method is then applied to ion crystals in a Penning trap. Reduced eigenvalue problems for the case of large applied magnetic field are developed, for which the spectrum breaks into ExB drift modes, axial modes, and cyclotron modes. Thermal fluctuation levels in these modes are analyzed and shown to be consistent with the Bohr-van-Leeuwen theorem, provided that neutrally-stable modes associated with crystal rotations are included in the analysis. An expression for the rotational inertia of the crystal is derived, and a magnetic contribution to this inertia, which dominates in large magnetic fields, is described. An unusual limit is discovered for the special case of spherically-symmetric confinement, in which the rotational inertia does not exist and changes in angular momentum leave the rotation frequency unaffected.
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