Phonon emission and absorption in the fractional quantum Hall effect

We investigate the time dependent thermal relaxation of a two-dimensional electron system in the fractional quantum Hall regime where ballistic phonons are used to heat up the system to a non-equilibrium temperature. The thermal relaxation of a 2DES at $\nu =1\mathrm{/}2$ can be described in terms of a broad band emission of phonons, with a temperature dependence proportional to $T^4$. In contrast, the relaxation at fractional filling $\nu =2\mathrm{/}3$ is characterized by phonon emission around a single energy, the magneto-roton gap. This leads to a strongly reduced energy relaxation rate compared to $\nu =1\mathrm{/}2$ with only a weak temperature dependence for temperatures 150 mK $<T<$ 400 mK.