Fedele Renato
Dipartimento di Scienze Fisiche, Universitá Federico II and INFN, Complesso Universitario di Monte S Angelo, Napoli, Italy.
Philos Trans A Math Phys Eng Sci. 2008 May 28;366(1871):1717-33. doi: 10.1098/rsta.2007.2181.
The impact of Maxwell's theory of Saturn's rings, formulated in Aberdeen ca 1856, is discussed. One century later, Nielsen, Sessler and Symon formulated a similar theory to describe the coherent instabilities (in particular, the negative mass instability) exhibited by a charged particle beam in a high-energy accelerating machine. Extended to systems of particles where the mutual gravitational attraction is replaced by the electric repulsion, Maxwell's approach was the conceptual basis to formulate the kinetic theory of coherent instability (Vlasov-Maxwell system), which, in particular, predicts the stabilizing role of the Landau damping. However, Maxwell's idea was so fertile that, later on, it was extended to quantum-like models (e.g. thermal wave model), providing the quantum-like description of coherent instability (Schrödinger-Maxwell system) and its identification with the modulational instability (MI). The latter has recently been formulated for any nonlinear wave propagation governed by the nonlinear Schrödinger equation, as in the statistical approach to MI (Wigner-Maxwell system). It seems that the above recent developments may provide a possible feedback to Maxwell's original idea with the extension to quantum gravity and cosmology.
本文讨论了麦克斯韦于1856年左右在阿伯丁提出的土星环理论的影响。一个世纪后，尼尔森、塞斯勒和西蒙提出了一个类似的理论，以描述高能加速机器中带电粒子束所表现出的相干不稳定性（特别是负质量不稳定性）。麦克斯韦的方法扩展到了粒子系统，其中粒子间的引力相互作用被电斥力所取代，它是建立相干不稳定性动力学理论（弗拉索夫 - 麦克斯韦系统）的概念基础，该理论特别预测了朗道阻尼的稳定作用。然而，麦克斯韦的思想极具创造性，后来它被扩展到类量子模型（如热波模型），提供了相干不稳定性的类量子描述（薛定谔 - 麦克斯韦系统）以及它与调制不稳定性（MI）的关联。后者最近已针对由非线性薛定谔方程描述的任何非线性波传播进行了阐述，就像在MI的统计方法（维格纳 - 麦克斯韦系统）中那样。上述最新进展似乎可能通过向量子引力和宇宙学的扩展，为麦克斯韦的原始思想提供一种可能的反馈。
