电子辐射反应的自洽动力学：通过保持结构的几何算法研究耦合薛定谔-麦克斯韦系统
Self-Consistent Dynamics of Electron Radiation Reaction via Structure-Preserving Geometric Algorithms for Coupled Schrödinger-Maxwell Systems
AI总结：
本文通过结构保持的几何算法研究耦合薛定谔-麦克斯韦系统，模拟电子相干态的辐射反应动力学及退相干过程，揭示了极端场环境下电子行为的新特性。
摘要：
经典上，带电粒子在磁场中发射辐射，损失动量并经历阿布里-洛伦兹（AL）/兰道-利夫希茨（LL）辐射反应（RR）力。然而，在原子尺度和其适用范围之外，AL/LL方程失效，RR破坏电子的相干态，从而削弱RR力的概念。这一过程可以通过适当的极限下的耦合薛定谔-麦克斯韦（SM）系统来描述，但系统非线性复杂性长期以来限制了纯粹的解析研究。我们提出了用于SM系统的几何结构保持算法，这些算法在离散时空晶格上保持规范不变性、辛性和幺正性，这些算法在我们的结构保持薛定谔-麦克斯韦（SPHINX）代码中实现。通过从朗道能级构造相干态，SPHINX模拟了电子相干态的完全耦合非线性动力学、能量分配演变以及由于RR导致的电子波包在时间上的退相干/弛豫。这些模拟表明，在外部磁场中，一个在原子尺度相干态中准备的电子可以强烈辐射，快速失去相干性并分散成一个退相干的波包。此外，我们还展示了非简并基态和第一激发朗道能级的完全耦合非线性演化，以了解耦合SM系统如何修改众所周知的理想（即仅薛定谔）的朗道能级动力学。通过适当的边界条件，模拟显示朗道能级被重整化为具有恒定电磁和动能能级的 stationary dressed eigenstates。这为RR物理开辟了新的计算窗口，并推进了在聚变等离子体、天体物理和下一代激光实验中的极端场现象建模。
英文摘要：
Classically, a charged particle in a magnetic field emits radiation, losing momentum and experiencing the Abraham-Lorentz (AL) / Landau-Lifshitz (LL) radiation reaction (RR) force. However, at atomic scales and outside the range of their applicability, the AL/LL equations fail and RR destroys the coherent state of an electron-undermining the very concept of a RR force. This process can be described by the coupled Schrödinger-Maxwell (SM) system under appropriate limits, but the system's nonlinear complexity has long limited purely analytical studies. We present geometric structure-preserving algorithms for the SM system that preserve gauge invariance, symplecticity, and unitarity on the discrete space-time lattice, which are implemented in our Structure-Preserving scHrodINger maXwell (SPHINX) code. By constructing coherent states from the Landau levels, SPHINX simulates the fully-coupled nonlinear dynamics of an electron coherent state, the energy partition evolution, and decoherence/relaxation of the electron wave packet in time due to RR. These simulations indicate that, in an external magnetic field, an electron prepared in an atomic-scale coherent state can radiate strongly, rapidly losing coherence and dispersing into a decoherent wave packet. Additionally, we also present the fully-coupled nonlinear evolution of the non-degenerate ground- and first-excited Landau levels themselves to understand how the coupled SM system modifies the well-known ideal (i.e., Schrödinger-only) dynamics of the Landau Levels. With appropriate boundary conditions, simulations show that the Landau levels are renormalized into stationary dressed eigenstates with constant electromagnetic and kinetic energies. This opens a new computational window into RR physics and advances modeling of extreme-field phenomena in fusion plasmas, astrophysics, and next-generation laser experiments
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