We study the unitary propagation of a two-particle one-dimensional Schrodinger equation by means of the Split-Step Fourier method, to study the coherent evolution of a spatially indirect exciton (IX) in semiconductor heterostructures. The mutual Coulomb interaction of the electron-hole pair and the electrostatic potentials generated by external gates and acting on the two particles separately are taken into account exactly in the two-particle dynamics. As relevant examples, step/downhill and barrier/well potential profiles are considered. The space- and time-dependent evolution during the scattering event as well as the asymptotic time behavior are analyzed. For typical parameters of GaAs-based devices the transmission or reflection of the pair turns out to be a complex two-particle process, due to comparable and competing Coulomb, electrostatic and kinetic energy scales. Depending on the intensity and anisotropy of the scattering potentials, the quantum evolution may result in excitation of the IX internal degrees of freedom, dissociation of the pair, or transmission in small periodic IX wavepackets due to dwelling of one particle in the barrier region. We discuss the occurrence of each process in the full parameter space of the scattering potentials and the relevance of our results for current excitronic technologies.
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