On the original Ulam's problem and its quantization

Series
CDSNS Colloquium
Time
Friday, March 7, 2025 - 3:30pm for 1 hour (actually 50 minutes)
Location
Skiles 314
Speaker
Jing Zhou – Great Bay University (Dongguan) – zhoujing@gbu.edu.cnhttps://www.gbu.edu.cn/detail/article/569?lang=en
Organizer
Alex Blumenthal

Please Note: Zoom link: https://gatech.zoom.us/j/91390791493?pwd=QnpaWHNEOHZTVXlZSXFkYTJ0b0Q0UT09

In 1961 Ulam proposed a mathematical simplification extracting the essential accelerating mechanism proposed by Fermi, as to explain the cause of high-energy particles in cosmic rays. In this talk, we shall describe the typical behavior of the very model introduced by Ulam in both the classical original form as well as its quantization. In the classical model, we show that typical orbits are recurrent under resonance assumptions. Meanwhile in the quantum model, the acceleration caused by resonance gets much amplified and we point out a direct relationship between the acceleration behavior of the system and the shape of its quasi-energy spectrum. This is a joint work in progress with Changguang Dong and Disheng Xu.