Leaky Fermi accelerators

TL;DR

This paper investigates how leaky Fermi accelerators, which are billiards with oscillating walls, transfer energy to an ideal gas through small holes, revealing that ergodic and multi-component accelerators differ in heat production.

Contribution

It introduces the concept of leaky Fermi accelerators and analyzes how their ergodic properties affect energy transfer to an environment.

Findings

Ergodic accelerators produce weaker energy flow than multi-component ones.

Energy gain in ergodic accelerators is independent of hole size.

Multi-component accelerators can significantly increase energy flow by reducing hole size.

Abstract

A Fermi accelerator is a billiard with oscillating walls. A leaky accelerator interacts with an environment of an ideal gas at equilibrium by exchange of particles through a small hole on its boundary. Such interaction may heat the gas: we estimate the net energy flow through the hole under the assumption that the particles inside the billiard do not collide with each other and remain in the accelerator for sufficiently long time. The heat production is found to depend strongly on the type of the Fermi accelerator. An ergodic accelerator, i.e. one which has a single ergodic component, produces a weaker energy flow than a multi-component accelerator. Specifically, in the ergodic case the energy gain is independent of the hole size, whereas in the multi-component case the energy flow may be significantly increased by shrinking the hole size.