Fermi acceleration in rotating drums

TL;DR

This paper investigates how Fermi acceleration occurs in rotating drums with gravity, providing explicit formulas and measure realizations for the system without gravity, highlighting the role of gravity in energy unboundedness.

Contribution

The paper introduces explicit formulas and measure realizations for the energy dynamics of balls in rotating drums, clarifying conditions for Fermi acceleration.

Findings

No Fermi acceleration without gravity

Fermi acceleration possible with gravity

Explicit formulas for system behavior

Abstract

Consider hard balls in a bounded rotating drum. If there is no gravitation then there is no Fermi acceleration, i.e., the energy of the balls remains bounded forever. If there is gravitation, Fermi acceleration may arise. A number of explicit formulas for the system without gravitation are given. Some of these are based on an explicit realization, which we derive, of the well-known microcanonical ensemble measure.