带电粒子在球体上运动的经典朗之万动力学和抗磁性：一个惊喜
Classical Langevin dynamics of a charged particle moving on a sphere and diamagnetism: A surprise
摘要：
众所周知，处于热平衡的经典带电粒子系统的轨道抗磁性为零--玻尔-范列文定理。物理上，这种零结果来自于与带电粒子的完整回旋轨道相关的轨道反磁矩被顺磁矩精确抵消，顺磁矩由在相反意义上跳过边界的不完整轨道所对。出于这个关键的，但微妙的作用的边界，我们在这里模拟的情况下，一个有限的，但\emph{unbounded}系统，即一个带电粒子在一个球体的表面上移动的存在下，外部施加的均匀磁场。按照基于经典朗之万方程的真实时空方法，我们计算了轨道磁矩，它现在确实是非零的，并具有抗磁符号。据我们所知，这是第一个报告的可能性有限的经典抗磁性的原则，这是由于避免取消。
英文摘要：
It is generally known that the orbital diamagnetism of a classical system of charged particles in thermal equilibrium is identically zero -- the Bohr-van Leeuwen theorem. Physically, this null result derives from the exact cancellation of the orbital diamagnetic moment associated with the complete cyclotron orbits of the charged particles by the paramagnetic moment subtended by the incomplete orbits skipping the boundary in the opposite sense. Motivated by this crucial, but subtle role of the boundary, we have simulated here the case of a finite but \emph{unbounded} system, namely that of a charged particle moving on the surface of a sphere in the presence of an externally applied uniform magnetic field. Following a real space-time approach based on the classical Langevin equation, we have computed the orbital magnetic moment which now indeed turns out to be non-zero, and has the diamagnetic sign. To the best of our knowledge, this is the first report of the possibility of finite classical diamagnetism in principle, and it is due to the avoided cancellation.
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