# A two-state generalisation of the strong collision model

## TL;DR

This paper introduces a two-state generalization of the strong collision model in muon spin relaxation, enabling better modeling of systems with discrete local field changes and broadening the technique's applicability.

## Contribution

A novel two-state strong collision model that explicitly accounts for transitions between distinct local field environments during fluctuations.

## Key findings

- Provides analytical and numerical solutions for the model.
- Demonstrates applicability to low-dimensional magnets and dynamic disorder.
- Extends the framework for interpreting complex dynamical phenomena.

## Abstract

Muon spin relaxation is a powerful technique for probing static and dynamic local magnetic fields. The strong collision model, based on a Gaussian-Markovian process, is commonly used to account for dynamical effects. Yet, it remains limited in describing systems where the local field undergoes discrete state changes. To address this, I introduce a generalized two-state strong collision model that explicitly incorporates transitions between distinct local field environments during fluctuations. This extension allows for a more accurate representation of dynamical effects, particularly in systems where each collision alters the underlying static polarisation function. Analytical and numerical solutions are presented, and the model's applicability is demonstrated and discussed across relevant physical systems -- including low-dimensional magnets, systems with dynamic disorder and ion and muon diffusion. These results offer an enhanced framework for interpreting data in complex materials and extend the method's reach to a broader class of dynamical phenomena in condensed matter physics.