Strongly confined fluids: Diverging time scales and slowing down of equilibration

The Newtonian dynamics of strongly confined fluids exhibits a rich behavior. Its confined and unconfined degrees of freedom decouple for confinement length L→0. In that case and for a slit geometry the intermediate scattering functions S_{μν}(q,t) simplify, resulting for (μ,ν)≠(0,0) in a Knudsen-gas-like behavior of the confined degrees of freedom, and otherwise in S_{∥}(q,t), describing the structural relaxation of the unconfined ones. Taking the coupling into account we prove that the energy fluctuations relax exponentially. For smooth potentials the relaxation times diverge as L^{-3} and L^{-4}, respectively, for the confined and unconfined degrees of freedom. The strength of the L^{-3} divergence can be calculated analytically. It depends on the pair potential and the two-dimensional pair distribution function. Experimental setups are suggested to test these predictions.