Jafari Amir
Johns Hopkins University, Department of Applied Mathematics and Statistics, The , Baltimore, Maryland, USA.
Phys Rev E. 2025 Jun;111(6-2):065212. doi: 10.1103/8cpp-fggq.
We employ well-known concepts from statistical physics, quantum field theories, and general topology to study magnetic reconnection and topology change and their connection in incompressible flows in the context of an effective field theory without appealing to magnetic field lines. We consider the dynamical system corresponding to wave packets moving with Alfvén velocity xover ̇:=V_{A}(x,t) whose trajectories x(t) define pathlines, which naturally provides a mathematical way to estimate the rate of magnetic topology change. A considerable simplification is attained, in fact, by directly employing well-known concepts from hydrodynamic turbulence without appealing to the complicated notion of magnetic field lines moving through plasma, which may prove even more useful in the relativistic regime. Continuity conditions for magnetic field allow rapid but continuous divergence of pathlines, shown to imply reconnection, but not discontinuous divergence, which would change topology. Thus, topology can change only due to time-reversal symmetry breaking, e.g., by dissipative effects. In laminar and even chaotic flows, the separation of pathlines at all times remains proportional to their initial separation, argued to correspond to slow reconnection, and topology changes by dissipation with a rate proportional to resistivity. In turbulence, pathlines diverge superlinearly with time independent of their initial separation, i.e., fast reconnection, and magnetic topology changes by turbulent dissipation with a rate independent of small-scale plasma effects. The crucial role of turbulence in enhancing topology change and reconnection rates originates from its ability to break time-reversal invariance and make the flow superchaotic. In fact, due to the loss of Lipschitz continuity of the magnetic field in turbulence, pathlines separate superlinearly even if their initial separation tends to vanish, unlike deterministic chaos. This superchaotic behavior is an example of spontaneous stochasticity in statistical physics, sometimes called the real butterfly effect in chaos theory to distinguish it from the butterfly effect, in which trajectories can diverge exponentially only if initial separation remains finite. If 3D reconnection is defined as magnetic topology change, it can be fast only in turbulence where both reconnection and topology change are driven by spontaneous stochasticity, independent of any plasma effects. Our results strongly support the Lazarian-Vishniac theory of turbulent reconnection.
我们运用统计物理学、量子场论和一般拓扑学中的知名概念，在有效场论的框架下研究磁重联和拓扑变化及其在不可压缩流中的联系，而无需借助磁力线。我们考虑与以阿尔文速度(x\dot{}:=V_{A}(x,t))移动的波包相对应的动力系统，其轨迹(x(t))定义了流线，这自然提供了一种估计磁拓扑变化率的数学方法。实际上，通过直接运用流体动力学湍流中的知名概念，而无需借助磁力线在等离子体中移动的复杂概念，实现了相当大的简化，这在相对论情形下可能更有用。磁场的连续性条件允许流线快速但连续地发散，这表明意味着重联，但不允许不连续发散，因为这会改变拓扑。因此，拓扑只能由于时间反演对称性破缺而改变，例如通过耗散效应。在层流甚至混沌流中，流线在任何时刻的分离始终与它们的初始分离成正比，这被认为对应于缓慢重联，并且拓扑通过耗散以与电阻率成正比的速率变化。在湍流中，流线随时间超线性发散，与它们的初始分离无关，即快速重联，并且磁拓扑通过湍流耗散以与小尺度等离子体效应无关的速率变化。湍流在增强拓扑变化和重联速率方面的关键作用源于其打破时间反演不变性并使流动超混沌的能力。实际上，由于湍流中磁场的李普希茨连续性的丧失，即使初始分离趋于消失，流线也会超线性分离，这与确定性混沌不同。这种超混沌行为是统计物理学中自发随机性的一个例子，在混沌理论中有时被称为真正的蝴蝶效应，以区别于蝴蝶效应，在蝴蝶效应中，只有当初始分离保持有限时，轨迹才能指数发散。如果将三维重联定义为磁拓扑变化，那么它只能在湍流中快速发生，在湍流中重联和拓扑变化都由自发随机性驱动，与任何等离子体效应无关。我们的结果有力地支持了拉扎里安 - 维什尼亚克湍流重联理论。
