发表机构
École polytechnique; Univ. Wien; Wolfgang Pauli Institute（巴黎综合理工学院; 维也纳大学; 沃尔夫冈·泡利研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文扩展了基于$L^2$的速率平均引理至电磁场下的Wigner方程，利用Stratonovich磁Wigner变换，在广义相空间中获得$L^2$紧致性，但无正则性提升。
AI 中文摘要
我们讨论了基于$L^2$的速率平均在Wigner动力学方程中的应用，该方程描述了受外部电磁场作用的粒子的密度算子的Wigner变换的量子演化。这将[F. Golse, J. Möller: Commun. Math. Sci. (2026)]中的基于$L^2$的平均引理扩展到电磁场情形。我们采用了Stratonovich [Sov. Phys. D., (1)414-418, 1956]提出的磁或规范不变的Wigner变换，该变换与通常定义的区别在于包含一个涉及磁矢势沿线段环量的相位因子。磁Wigner变换在广义相空间变量$(x,v=\xi-A(t,x))$中满足Wigner方程，这是应用速率平均的更自然设置。由于磁Wigner方程包含空间变量的一阶导数，我们获得了$L^2$中的紧致性，但没有正则性的提升。
英文摘要
We discuss the application of $L^2$-based velocity averaging to the Wigner kinetic equation governing the quantum evolution of the Wigner transform of a density operator of a particle subjected to an external electromagnetic field. This extends the $L^2$-based averaging lemma from [F. Golse, J. Möller: Commun. Math. Sci. (2026)] to electromagnetic fields. We make use of the magnetic or gauge-invariant Wigner transform due to Stratonovich [Sov. Phys. D., (1)414-418, 1956] which differs from the usual definition by a phase factor involving the circulation of the magnetic vector potential along a line segment. The magnetic Wigner transform obeys the Wigner equation in the generalized phase space variables $(x,v=ξ-A(t,x))$, which is a more natural setting for the application of velocity averaging. Since the magnetic Wigner equation contains a first order derivative in the spatial variable, we obtain compactness in $L^2$ but no gain in regularity.
