标题： 关于原始乌拉姆问题及其量化 显示英文标题

标题： On the original Ulam's problem and its quantization

摘要： 在本文中，我们表明在一般共振条件下，经典的分段线性费米-乌拉姆加速器的行为与它的量子化版本显著不同，即经典加速器表现出典型的回归和不逃逸特性，而量子版本则通常表现出二次能量增长。 我们还描述了一种定位逃逸轨道的方法，尽管在无限体积相空间中这些轨道极其罕见，但经典加速器包括乌拉姆最初提出的方案以及现有文献中其中的线性逃逸轨道，因此为乌拉姆最初的问题提供了一个完整的（模零集）答案。 对于量子加速器，我们在共振条件下揭示了能量增长与准能量谱形状之间的直接和显式联系。 显示英文摘要

摘要： In this paper we show that under general resonance the classical piecewise linear Fermi-Ulam accelerator behaves substantially different from its quantization in the sense that the classical accelerator exhibits typical recurrence and non-escaping while the quantum version enjoys quadratic energy growth in general. We also describe a procedure to locate the escaping orbits, though exceptionally rare in the infinite-volume phase space, for the classical accelerators, which in particular include Ulam's very original proposal and the linearly escaping orbits therein in the existing literature, and hence provide a complete (modulo a null set) answer to Ulam's original question. For the quantum accelerators, we reveal under resonance the direct and explicit connection between the energy growth and the shape of the quasi-energy spectra.