# Thermo-quantum diffusion in periodic potentials

## TL;DR

This paper investigates quantum diffusion in periodic potentials, showing that heavy particles follow semiclassical estimates while electrons exhibit purely quantum behavior with non-classical dispersion growth at zero temperature.

## Contribution

It introduces a semiclassical approach for quantum Brownian motion in periodic potentials and highlights the limitations for electrons due to dominant quantum effects.

## Key findings

- Heavy particles follow semiclassical tunneling estimates.
- Electrons do not obey classical Brownian motion laws.
- Electron wave packet dispersion grows logarithmically over time.

## Abstract

Quantum Brownian motion in a periodic cosine potential is studied and a simple estimate of the tunneling effect is obtained in the frames of a quasi-equilibrium semiclassical approach. It is shown that the latter is applicable for heavy particles but electrons cannot be described properly since the quantum effects dominate over the thermal ones. The purely quantum electron diffusion is investigated at zero temperature and demonstrates that electrons do not obey the classical Einstein law of Brownian motion in the field of periodic potentials, since the dispersion of the wave packet increases logarithmically in time.

---
Source: https://tomesphere.com/paper/0912.1488