# Composite quantum collision models

## TL;DR

This paper introduces a general framework for memoryless composite collision models in quantum dynamics, enabling the modeling of complex non-Markovian behaviors through internal and external system-ancilla interactions.

## Contribution

It extends collision models to include composite systems with internal and external collisions, capturing a wider range of non-Markovian quantum phenomena.

## Key findings

- Maps non-Markovian dynamics to memoryless composite collision models
- Includes models with Lorentzian spectral densities and telegraph noise
- Provides a unified framework for complex open quantum systems

## Abstract

A collision model (CM) is a framework to describe open quantum dynamics. In its {\it memoryless} version, it models the reservoir $\mathcal R$ as consisting of a large collection of elementary ancillas: the dynamics of the open system $\mathcal{S}$ results from successive "collisions" of $\mathcal{S}$ with the ancillas of $\mathcal R$. Here, we present a general formulation of memoryless {\it composite} CMs, where $\mathcal S$ is partitioned into the very open system under study $S$ coupled to one or more auxiliary systems $\{S_i\}$. Their composite dynamics occurs through internal $S$-$\{S_i\}$ collisions interspersed with external ones involving $\{S_i\}$ and the reservoir $\mathcal R$. We show that important known instances of quantum {\it non-Markovian} dynamics of $S$ -- such as the emission of an atom into a reservoir featuring a Lorentzian, or multi-Lorentzian, spectral density or a qubit subject to random telegraph noise -- can be mapped on to such {\it memoryless} composite CMs.