[论文解读] Self-Consistent Dynamics of Electron Radiation Reaction via Structure-Preserving Geometric Algorithms for Coupled Schrödinger-Maxwell Systems

Jacob Matthew Molina, Hong Qin|arXiv (Cornell University)|Feb 19, 2026

Laser-Plasma Interactions and Diagnostics被引用 0

一句话总结

该论文开发了结构保持几何算法，以在耦合的 Schrödinger-Maxwell 系统中自洽地模拟辐射反应，实现在 SPHINX 中，并分析在磁场中的电子相干性和朗道能级。

ABSTRACT

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

研究动机与目标

• 以自洽电磁场描述的波函数量子电子的辐射反应为动机并进行研究
• 在时空格点上开发离散的、结构保持的 Schrödinger-Maxwell（SM）框架，保持规范不变性、辛性和单位性
• 在 SPHINX 代码中实现这些算法，以研究电子相干态的非线性动力学以及辐射反应导致的去相干性。

提出的方法

• 推导离散 Schrödinger-Maxwell 动力学并在空间网格上离散化规范泊松结构
• 将离散哈密顿量分解为量子部分和电磁部分，并应用辛中点时间积分
• 使用 Cayley 变换传播离散的量子变量和场变量，同时保持辛性与幺正演化
• 从朗道能级本征态构建相干态，以在均匀磁场中初始化电子的模拟
• 模拟完全耦合的非线性动力学，以观察能量分配、去相干和朗道能级的重整化
• 提供考虑边界条件的模拟，演示耦合系统中的驻留 dressed 本征态。

实验结果

研究问题

• RQ1 自洽地让带有波函数的量子电子在自身电磁场中辐射反应作用下如何演化？
• RQ2 结构保持的几何算法是否能够可靠地在保持规范不变性、辛性和单位性的前提下，模拟完全耦合的 Schrödinger-Maxwell 系统？
• RQ3 辐射反应对外场磁场中原子尺度电子的相干性与能量分配有何影响？
• RQ4 在完全耦合的非线性 SM 动力学中，朗道能级如何被修改，是否在适当边界条件下出现驻留的 dressed 本征态？

主要发现

• 在外部磁场中的原子尺度相干态在考虑辐射反应时会强烈辐射并快速失去轨道相干性，演化为去相干的波包
• 耦合的 SM 动力学会修改朗道能级本征态，在适当边界条件下可以保持为驻留的 dressed 本征态，且电磁能量与动能保持常数
• SPHINX 代码展示了电子波函数与电磁场的完全自洽非线性演化，使极端场强度下的 RR 物理成为可能
• 结构保持算法在整个离散格点上保持规范不变性、辛性和单位性
• 朗道能级被重整化为驻留的 dressed 本征态，为耦合电子-光子系统提供了自然基底