A hard-sphere model on generalised Bethe lattices: Dynamics

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We analyse the dynamics of a hard-sphere lattice gas on generalised Bethe lattices using a projective approximation scheme (PAS). The latter consists in mapping the system's dynamics to a finite set of global observables, closure of the resulting equations is obtained by approximating the true non-equilibrium state by a pseudo-equilibrium based only on the value of the observables under consideration. We study the liquid--crystal as well as the liquid--spin-glass transitions, special attention is given to the prediction of equilibration times and their divergence close to the phase transitions. Analytical results are corroborated by Monte-Carlo simulations.