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We theoretically investigate the evolution of the peak height of an energyresolved electronic wave-packets ballistically propagating along integerquantum Hall edge channels at filling factor $\nu=2$. This is ultimatelyrelated to the elastic scattering amplitude for the fermionic excitationsevaluated at different injection energy. We investigate this quantity assuminga short range capacitive coupling between the edges. Moreover, we also takeinto account phenomenologically the possibility of energy dissipation towardsadditional degrees of freedom both linear and quadratic in the injectionenergy. Comparing with recent experimental data, we rule out thenon-dissipative case as well a quadratic dependence of the dissipation,indicating a linear energy loss rate as the best candidate to describe thebehavior of the quasi-particle peak at short enough propagation lengths.

Electronic wave-packets in integer quantum Hall edge channels: relaxation and dissipative effects