Hello everybody, I have a question related to dispersionless excitations in solids (especially charge excitations). Usually when you have a charge excitation involving an impurity in a solid or another excitation that is very local in real space, they show up with a flat dispersion in reciprocal space. First of all, it's not really straightforward for me to understand why. Is it due to the fact that we can assume a zero Fermi velocity? The second question I have is related to the nature of this kind of excitations. If a charge excitation is very local in real space, I would expect a strong excitonic nature, as a Frenkel exciton. This happens for instance in optically forbidden d-d transitions, whose dispersion can be probed by resonant inelastic x-ray scattering (RIXS). Therefore, the dispersion I expect to be flat is the one of the two-particle excitation spectrum. However, many times, I also see in ARPES measurements that a flat dispersion appears for impurity states in solids. ARPES is sensitive to the single-particle excitation spectrum and it involves a process that is completely different with respect to RIXS. How can this flat dispersion be retrieved also in the single-particle scenario in the case of impurity states? Thanks for your time.