A two-state generalisation of the strong collision model

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.