标题： 磁通锥上的经典与量子运动方面 显示英文标题

标题： Aspects of classical and quantum motion on a flux cone

摘要： 研究了非相对论粒子在一个具有沿锥轴磁通量的圆锥上的运动（即“磁通锥”）。该运动被表述为粒子在欧几里得平面上受速度相关力作用下的运动。 研究了与特定定态相关的概率流体（“量子流”）在奇点附近的性质，展示了非平凡的阿哈罗诺夫-玻姆效应。例如，证明了在奇点附近，量子流不同于经典流。 在量子力学的流体力学方法的背景下，确定了由于锥形奇点引起的量子势，并分析了它如何影响量子流。还表明经典轨道的缠绕数在描述量子流时起着重要作用。 此外，还讨论了构型空间的连通性。 显示英文摘要

摘要： Motion of a non-relativistic particle on a cone with a magnetic flux running through the cone axis (a ``flux cone'') is studied. It is expressed as the motion of a particle moving on the Euclidean plane under the action of a velocity-dependent force. Probability fluid (``quantum flow'') associated with a particular stationary state is studied close to the singularity, demonstrating non trivial Aharonov-Bohm effects. For example, it is shown that near the singularity quantum flow departs from classical flow. In the context of the hydrodynamical approach to quantum mechanics, quantum potential due to the conical singularity is determined and the way it affects quantum flow is analysed. It is shown that the winding number of classical orbits plays a role in the description of the quantum flow. Connectivity of the configuration space is also discussed.