Third order susceptibilities in supercooled liquids and the "box model" theory versus experiments

We give here the exact expression of the time dependent third order polarization predicted by the "box model" when a supercooled liquid is permanently subjected since time t = 0 to a strong electric field E(t) = E(0) sin(ωt), Dielectric Hole Burning experiment. We derive different forms of the time dependent susceptibilities, both at frequencies ω and 3ω, and examine particularly one of them. We also show that its susceptibility at ω should exhibit, at short times, presently undetected oscillations at frequency 2ω that are a signature of the "box model." We finally compare, for a large frequency range, the ω and 3ω time independent susceptibilities with the corresponding measurements on glycerol at 204.7 K. The agreement is good at frequency ω but, as already shown in Ladieu et al. [J. Chem. Phys. 134, 194507 (2011)], it is not the case at 3ω.