de Moura Alessandro P S, Grebogi Celso
Institute for Plasma Research, Department of Mathematics, Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Mar;65(3 Pt 2A):035206. doi: 10.1103/PhysRevE.65.035206. Epub 2002 Mar 1.
We study the effects of classical chaotic scattering on the differential cross section, which is the measurable quantity in most scattering experiments. We show that the fractal set of singularities in the deflection function is not, in general, reflected on the differential cross section. We show that there are systems in which, as the energy (or some other parameter) crosses a critical value, the system's differential cross-section changes from a singular function having an infinite set of rainbow singularities with structure in all scales to a smooth function with no singularities, the scattering being chaotic on both sides of the transition. We call this metamorphosis the rainbow transition. We exemplify this transition with a physically relevant class of systems. These results have important consequences for the problem of inverse scattering in chaotic systems and for the experimental observation of chaotic scattering.
我们研究了经典混沌散射对微分截面的影响，微分截面是大多数散射实验中可测量的量。我们表明，一般来说，偏转角函数中的奇点分形集不会反映在微分截面上。我们表明，存在这样的系统，当能量（或其他一些参数）越过临界值时，系统的微分截面从具有无穷多组不同尺度结构的彩虹奇点的奇异函数变为无奇点的光滑函数，并且在转变两侧散射都是混沌的。我们将这种转变称为彩虹转变。我们用一类具有物理相关性的系统来例证这种转变。这些结果对于混沌系统中的逆散射问题以及混沌散射的实验观测具有重要意义。
