We perform explicit time-dependent classical and quantum propagation of a spatially indirect exciton (SIX) driven by surface acoustic waves (SAWs) in a semiconductor heterostructure device. We model the SIX dynamics at different levels of description, from the Euler-Lagrange propagation of structureless classical particles to unitary Schrodinger propagation of an electron-hole wave packet in a mean field and to the full quantum propagation of the two-particle complex. A recently proposed beyond mean-field self-energy approach, adding internal virtual transitions to the c.m. dynamics, has been generalized to time-dependent potentials and turns out to describe very well full quantum calculations, while being orders of magnitude numerically less demanding. We show that SAW-driven SIXs are a sensitive probe of scattering potentials in the devices originating, for example, from single impurities or metallic gates, due to competing length and energy scales between the SAW elastic potential, the scattering potential, and the internal electron-hole dynamic of the SIX. Comparison between different approximations allow us to show that internal correlation of the electron-hole pair is crucial in scattering from shallow impurities, where tunneling plays a major role. On the other hand, scattering from broad potentials, i.e., with length scales exceeding the SIX Bohr radius, is well described as the classical dynamics of a pointlike SIX. Recent experiments are discussed in light of our calculations.
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