# A Rectangular Billiard with Moving Slits

## TL;DR

This paper introduces a two-dimensional billiard model with a moving slit that acts as an exponential Fermi accelerator, demonstrating a trapping mechanism that leads to exponential energy gain for most high-energy initial conditions.

## Contribution

It presents a novel billiard system with a moving slit that causes exponential acceleration, along with an estimation of the waiting time for energy growth under hyperbolicity.

## Key findings

- Most high-energy orbits gain energy exponentially fast.
- A trapping mechanism enables exponential acceleration.
- Waiting time estimates for energy growth under hyperbolicity.

## Abstract

We describe an exponential Fermi accelerator in a two-dimensional billiard with a moving slit. We have found a mechanism of trapping regions which provides the exponential acceleration for almost all initial conditions with sufficiently high initial energy. Under an additional hyperbolicity assumption, we estimate the waiting time after which most high-energy orbits start to gain energy exponentially fast.