Quantum Hall edge channels offer an efficient and controllable platform to study quantum transport in one dimension. Such channels are a prospective tool for the efficient transfer of quantum information at the nanoscale, and play a vital role in exposing intriguing physics. Electric current along the edge carries energy and heat leading to inelastic scattering, which may impede coherent transport. Several experiments attempting to probe the concomitant energy redistribution along the edge reported energy loss via unknown mechanisms of inelastic scattering. Here we employ quantum dots to inject and extract electrons at specific energies, to spectrally analyse inelastic scattering inside quantum Hall edge channels. We show that the missing energy puzzle could be untangled by incorporating non-local Auger-like processes, in which energy is redistributed between spatially separate parts of the sample. Our theoretical analysis, accounting for the experimental results, challenges common-wisdom analyses which ignore such non-local decay channels.

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This work concerns the concentration dependence of the optical properties of microscale samples according to the solid solution Li2Ca1–2xPrxNaxSiO4 with x = 0.001, 0.002, 0.005, 0.01, 0.02, 0.05, 0.07, and 0.1. Phase purity was inspected by using X-ray powder diffraction. In order to figure out concentration dependent similarities and differences of their properties with respect to down- and up-conversion, luminescence spectroscopy for vacuum UV (VUV), X-ray, and blue light excitation were performed. Furthermore, diffuse reflection spectroscopy as well as time dependent luminescence measurements were conducted. It turns out that the concentration quenching of the up-conversion lags the down-conversion. In addition, a rise time can be observed in the time dependent measurements of the up-conversion. From these observations, it is concluded that the up-conversion process takes place via an energy transfer process with a very high probability.