论文标题
动能和磁矩的划分
Partition of kinetic energy and magnetic moment in dissipative diamagnetism
论文作者
论文摘要
在本文中，我们分析了耗散性的diamagnetism，这是根据量子偶联定理的量子对应物在二维中以二维运动为二维引起的。我们考虑在存在均匀磁场的情况下，在谐波井中移动的带电量子粒子，并耦合到量子热浴中，该量子被视为由无限数量的独立量子振荡器组成。量子能量均衡定理告诉我们，可以表达耗散振荡器的平均动能为两倍的平均值，在此，在吉布斯的吉布斯典型状态下进行第一个平均，而第二个平均值则由第二个平均值执行，而第二个平均值则由概率分布函数$ p_k（ω）$。我们进一步分析了该结果，并证明了其在弱耦合极限中的一致性。在此之后，我们计算系统的平衡磁矩，并揭示了与量子电气定理的量子相对的有趣联系。动能和磁矩的表达在超级巨星的背景下重新制定，即两个统计数据的叠加。对本结果的比较研究与从更传统的吉布斯方法中获得的结果进行了比较研究，并获得了完美的一致性。
In this paper, we analyze dissipative diamagnetism, arising due to dissipative cyclotron motion in two dimensions, in the light of the quantum counterpart of energy equipartition theorem. We consider a charged quantum particle moving in a harmonic well, in the presence of a uniform magnetic field, and coupled to a quantum heat bath which is taken to be composed of an infinite number of independent quantum oscillators. The quantum counterpart of energy equipartition theorem tells us that it is possible to express the mean kinetic energy of the dissipative oscillator as a two-fold average, where, the first averaging is performed over the Gibbs canonical state of the heat bath while the second one is governed by a probability distribution function $P_k(ω)$. We analyze this result further, and also demonstrate its consistency in the weak-coupling limit. Following this, we compute the equilibrium magnetic moment of the system, and reveal an interesting connection with the quantum counterpart of energy equipartition theorem. The expressions for kinetic energy and magnetic moment are reformulated in the context of superstatistics, i.e. the superposition of two statistics. A comparative study of the present results with those obtained from the more traditional Gibbs approach is performed and a perfect agreement is obtained.
