论文标题
正常模式，旋转惯性和被困离子晶体的热波动
Normal Modes, Rotational Inertia, and Thermal Fluctuations of Trapped Ion Crystals
论文作者
论文摘要
使用基于系统动力学矩阵的Hermitian特性的方法得出了捕获离子晶体的正常模式。该方法等同于标准的Bogoliubov方法，但是对于经典系统，可以说更简单，更通用，因为规范坐标是不需要的。该理论是为稳定，不稳定且中立稳定的系统而开发的。然后将该方法应用于笔陷阱中的离子晶体。开发了大型施加磁场情况的特征值问题，为此，频谱分解为EXB漂移模式，轴向模式和回旋体模式。分析这些模式中的热波动水平与Bohr-Van-Leeuwen定理一致，前提是分析中包括与晶体旋转相关的中性稳定模式。得出了晶体旋转惯性的表达，并描述了在大型磁场中占主导地位的惯性的磁性贡献。对于球形对称限制的特殊情况，发现了异常的极限，其中不存在旋转惯性，并且角动量的变化使旋转频率不受影响。
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.
