论文标题
静态磁场对古典布朗运动的持久影响
Lasting effects of static magnetic field on classical Brownian motion
论文作者
论文摘要
Bohr-van Leeuwen定理指出，外部静态磁场不影响经典平衡系统的状态：由于磁场不起作用，因此没有平衡的经典磁性。我们重新审视了这个著名的无需结果，并考虑了经典的带电的布朗粒子与平衡浴室相互作用。我们确认Bohr-Van Leeuwen定理具有长期（平衡）粒子状态。但是外部静态均匀的磁场确实会影响热浴的长期状态，这是通过Caldeira-Leggett模型描述的。特别是，磁场会引起（未充电！）浴的平均角动量，该浴场分为两组朝相反的方向旋转。该效果与浴缸在布朗粒子的影响下略有脱离平衡有关，并任意长时间持续。在这种情况下，我们研究了其他两个运动，能量和线性动量的添加剂积分的行为。线性动量的情况不同，因为它被浴缸模式消失了。浴模式的平均能量将磁场保留为较小的校正。因此，只有浴缸动量才真正感觉到磁场很长时间。
The Bohr-Van Leeuwen theorem states that an external static magnetic field does not influence the state of a classical equilibrium system: there is no equilibrium classical magnetism, since the magnetic field does not do work. We revisit this famous no-go result and consider a classical charged Brownian particle interacting with an equilibrium bath. We confirm that the Bohr-Van Leeuwen theorem holds for the long-time (equilibrium) state of the particle. But the external static, homogeneous magnetic field does influence the long-time state of the thermal bath, which is described via the Caldeira-Leggett model. In particular, the magnetic field induces an average angular momentum for the (uncharged!) bath, which separates into two sets rotating in opposite directions. The effect relates to the bath going slightly out of equilibrium under the influence of the Brownian particle and persists for arbitrarily long times. In this context we studied the behavior of the two other additive integrals of motion, energy and linear momentum. The situation with linear momentum is different, because it is dissipated away by (and from) the bath modes. The average energy of the bath mode retains the magnetic field as a small correction. Thus, only the bath angular momentum really feels the magnetic field for long times.
