曲面上带电粒子经典抗磁性的不存在性和非平衡涨落定理
Nonexistence of classical diamagnetism and nonequilibrium fluctuation theorems for charged particles on a curved surface
摘要：
我们证明了在与时间无关的磁场中，封闭曲面上带电粒子的经典朗之万动力学导致了长时间极限下的正则分布。因此，玻尔-范列文定理甚至对没有任何边界的有限系统也成立，并且平均磁矩为零。这与Kumar和Kumar（EPL，{ \bf 86}（2009）17001）最近从朗之万动力学的数值分析中获得的主张相反，该主张认为，在存在磁场的情况下，球体表面上的经典带电粒子具有非零的平均抗磁矩。我们将我们的分析扩展到曲面上的多粒子系统，并证明了非平衡涨落定理在这种几何中也成立。
英文摘要：
We show that the classical Langevin dynamics for a charged particle on a closed curved surface in a time-independent magnetic field leads to the canonical distribution in the long time limit. Thus the Bohr-van Leeuwen theorem holds even for a finite system without any boundary and the average magnetic moment is zero. This is contrary to the recent claim by Kumar and Kumar (EPL, {\bf 86} (2009) 17001), obtained from numerical analysis of Langevin dynamics, that a classical charged particle on the surface of a sphere in the presence of a magnetic field has a nonzero average diamagnetic moment. We extend our analysis to a many-particle system on a curved surface and show that the nonequilibrium fluctuation theorems also hold in this geometry.
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