# A model for Faraday pilot waves over variable topography

## TL;DR

This paper presents a hydrodynamic model that captures the interaction between bouncing droplets and variable topography, reproducing phenomena like reflection and diffraction observed in pilot-wave experiments.

## Contribution

A new reduced hydrodynamic model that quantitatively describes droplet interactions with variable topography in pilot-wave systems.

## Key findings

- Model reproduces non-specular reflection.
- Model captures single-slit diffraction.
- Quantitative agreement with key experiments.

## Abstract

Couder and Fort discovered that droplets walking on a vibrating bath possess certain features previously thought to be exclusive to quantum systems. These millimetric droplets synchronize with their Faraday wavefield, creating a macroscopic pilot-wave system. In this paper we exploit the fact that the waves generated are nearly monochromatic and propose a hydrodynamic model capable of quantitatively capturing the interaction between bouncing drops and a variable topography. We show that our reduced model is able to reproduce some important experiments involving the drop-topography interaction, such as non-specular reflection and single-slit diffraction.