# Stochastic webs and quantum transport in superlattices: an introductory review

## TL;DR

This review explores how stochastic webs facilitate quantum transport in semiconductor superlattices under electric and magnetic fields, highlighting recent modifications to enhance chaotic transport and potential applications.

## Contribution

It provides an introductory overview of stochastic webs in low-dimensional systems and discusses a new modification to improve chaotic transport in superlattices.

## Key findings

- Stochastic webs enable transport from low to high energies in phase space.
- A new modification of stochastic webs can enhance chaotic transport.
- Potential applications of enhanced transport in superlattice devices.

## Abstract

Stochastic webs were discovered, first by Arnold for multi-dimensional Hamiltonian systems, and later by Chernikov et al. for the low-dimensional case. Generated by weak perturbations, they consist of thread-like regions of chaotic dynamics in phase space. Their importance is that, in principle, they enable transport from small energies to high energies. In this introductory review, we concentrate on low-dimensional stochastic webs and on their applications to quantum transport in semiconductor superlattices subject to electric and magnetic fields. We also describe a recently-suggested modification of the stochastic web to enhance chaotic transport through it and we discuss its possible applications to superlattices. keywords: stochastic webs; quantum transport; superlattices; separatrix chaos