AI 中文总结
本文针对缺乏正则哈密顿形式的非完整力学系统，将其量子化为马尔可夫开放量子系统，找到对应Chaplygin雪橇和Suslov问题经典动力学的林德布拉德超算符，数值验证协方差符合亚稳态理论预测。
AI 中文摘要
非完整力学描述受非可积速度约束的系统，如滚动体和滑冰运动，这类系统通常缺乏正则哈密顿形式，阻碍了标准量子化方法的应用。本文将非完整系统量子化为马尔可夫开放量子系统，非完整约束出现在大耗散极限中。我们找到了明确的林德布拉德超算符，能在半经典极限下重现Chaplygin雪橇和Suslov问题的经典动力学。对主方程进行数值模拟，结果显示协方差满足开放量子系统亚稳态理论预测的关系。
英文摘要
Nonholonomic mechanics describes systems subject to non-integrable velocity constraints, such as rolling bodies and skating motion. These systems generally lack a canonical Hamiltonian formulation, obstructing standard quantization methods. Here we quantize nonholonomic systems as Markovian open quantum systems, with the nonholonomic constraint appearing in a large-dissipation limit. We find explicit Lindblad superoperators that reproduce the classical dynamics of the Chaplygin sleigh and the Suslov problem in the semiclassical limit. The master equation is numerically simulated, and the covariance is shown to satisfy a relation predicted by the theory of metastability in open quantum systems.
Comments11 pages, 3 figures
