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Modeling electron dynamics coupled to continuum states in finite volumes

Absorbing boundaries are frequently employed in real-time propagation of the Schrödinger equation to remove spurious reflections and efficiently emulate outgoing boundary conditions. These conditions are a fundamental ingredient for an implicit description of observables involving infinitely extended continuum states. In the literature, several boundary absorbers have been proposed. They mostly fall into three main families: mask function absorbers, complex absorbing potentials, and exterior complex-scaled potentials. To date none of the proposed absorbers is perfect, and all present a certain degree of reflections. Characterization of such reflections is thus a critical task with strong implications for time-dependent simulations of atoms and molecules. We introduce a method to evaluate the reflection properties of a given absorber and present a comparison of selected samples for each family of absorbers. Further, we discuss the connections between members of each family and show how the same reflection curves can be obtained with very different absorption schemes.