Theory for the dynamics of glassy mixtures with particle size swaps

We present a theory for the dynamics of a binary mixture with particle size swaps. The theory is based on a factorization approximation similar to that employed in the mode-coupling theory of glassy dynamics. The theory shows that, in accordance with physical intuition, particle size swaps open up an additional channel for the relaxation of density fluctuations. Thus, allowing swaps speeds up the dynamics and moves the dynamic glass transition towards higher densities and/or lower temperatures. We calculate an approximate dynamic glass transition phase diagram for an equimolar binary hard sphere mixture. We find that in the presence of particle size swaps, with increasing ratio of the hard sphere diameters the dynamic glass transition line moves towards higher volume fractions, up to the ratio of the diameters approximately equal to 1.2, and then saturates. We comment on the implications of our findings for the theoretical description of the glass transition.