Three particles on a ring

✍ Scribed by F. Rabouw; Th.W. Ruijgrok

• Book ID: 103892267
• Publisher: Elsevier Science
• Year: 1981
• Tongue: English
• Weight: 604 KB
• Volume: 109
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(81)90008-x

✦ Synopsis

We study the ergodic properties of three classical particles of unequal mass moving on a ring and colliding like hard points.

Although it is generally believed that this system is ergodic, we show that extensive numerical calculations do not support this belief.

This may be connected with our discovery that for vanishing total momentum, any initial state with one particle at rest is periodic, independent of the mass values.

The analogous periodicity for two unequal mass particles bouncing in a one-dimensional box can be understood on the basis of a remarkable property of a billiard in the form of a rectangular triangle.