# Reduced and Extended Weak Coupling Limit

## TL;DR

This paper reviews recent advances in the extended weak coupling limit, focusing on the mathematical framework of completely positive semigroups and their dilations, and introduces a simplified construction of quadratic noises.

## Contribution

It provides an extended review and a simplified construction method for quadratic noises within the extended weak coupling limit framework.

## Key findings

- Clarified the mathematical structure of the extended weak coupling limit.
- Presented an easier construction of quadratic noises.
- Enhanced understanding of completely positive semigroups and their dilations.

## Abstract

We give an extended review of recent work on the extended weak coupling limit. Background material on completely positive semigroups and their unitary dilations is given, as well as a particularly easy construction of `quadratic noises'.