Newtonian Kinetic Theory and the Ergodic-Nonergodic Transition

作者：Das Shankar P^*; Mazenko Gene F

来源：Journal of Statistical Physics, 2013, 152(1): 159-194.

DOI：10.1007/s10955-013-0755-3

• Martin-Siggia-Rose (MSR) field-theory
• Newtonian dynamics
• Ergodic-nonergodic transition
• Fluctuation-dissipation theorem

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 rho, 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.

• 出版日期2013-7