# Continuous-time random walk for a particle in a periodic potential

## TL;DR

This paper derives a continuous-time random walk model for a Brownian particle in a deep periodic potential, providing analytical expressions for waiting times and jump lengths, and validates it with experiments on Cesium atoms in an optical lattice.

## Contribution

The paper microscopically derives a CTRW model for particles in periodic potentials and validates it experimentally without free parameters.

## Key findings

- Excellent agreement between theory and experiment.
- Analytical expressions for waiting-time and jump-length distributions.
- Model accurately describes underdamped diffusion in optical lattices.

## Abstract

Continuous-time random walks offer powerful coarse-grained descriptions of transport processes. We here microscopically derive such a model for a Brownian particle diffusing in a deep periodic potential. We determine both the waiting-time and the jump-length distributions in terms of the parameters of the system, from which we analytically deduce the non-Gaussian characteristic function. We apply this continuous-time random walk model to characterize the underdamped diffusion of single Cesium atoms in a one-dimensional optical lattice. We observe excellent agreement between experimental and theoretical characteristic functions, without any free parameter.