# Theory for the single-particle dynamics in glassy mixtures with particle size swaps

## TL;DR

This paper develops a theoretical framework for understanding how particle size swaps influence single-particle dynamics in glassy mixtures, revealing that swaps accelerate relaxation and increase cage size, with predictions aligning with mode-coupling theory.

## Contribution

The paper introduces a mode-coupling-like theory for single-particle dynamics in glassy mixtures with particle size swaps, extending previous collective dynamics models.

## Key findings

- Particle size swaps speed up both collective and single-particle relaxation.
- The theory predicts an increased cage size in systems with particle size swaps.
- Single-particle motion becomes arrested at the same glass transition as collective dynamics.

## Abstract

We present a theory for the single-particle dynamics in binary mixtures with particle size swaps. The general structure of the theory follows that of the theory for the collective dynamics in binary mixtures with particle size swaps, which we developed previously [G. Szamel, Phys. Rev. E 98, 050601(R) (2018)]. Particle size swaps open up an additional relaxation channel, which speeds up both the collective dynamics and the single-particle dynamics. To make explicit predictions, we resort to a factorization approximation similar to that employed in the mode-coupling theory of glassy dynamics. We show that, like in the standard mode-coupling theory, the single-particle motion becomes arrested at the dynamic glass transition predicted by the theory for the collective dynamics. We compare the non-ergodicity parameters predicted by our mode-coupling-like approach for the an equimolar binary hard sphere mixture with particle size swaps with the non-ergodicity parameters predicted by the standard mode-coupling theory for the same system without swaps. Our theory predicts that the "cage size" is bigger in the system with particle size swaps.