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 $L\to 0$. In that case and for a slit geometry the intermediate scattering functions $S_{\mu \nu }(q,t)$ simplify, resulting for $(\mu ,\nu )\ne (0,0)$ in a Knudsen-gas-like behavior of the confined degrees of freedom, and otherwise in $S_{\parallel }(q,t)$, 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.