Newtonian Kinetic Theory and the Ergodic-Nonergodic Transition

In a recent work we have discussed how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective interaction potential. In the present work we use this development for investigating ergodic-nonergodic (ENE) transitions in dense fluids. The theory is developed in terms of a core problem spanned by the variables $ρ$, the number density, and $B$, a response density. We set up the perturbation theory expansion for studying the self-consistent model which gives rise to a ENE transition. Our main result is that the low-frequency dynamics near the ENE transition is the same for Smoluchowski and Newtonian dynamics. This is true despite the fact that term by term in a density expansion the results for the two dynamics are fundamentally different.

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