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How would you define an absorbing region (at the walls of a finite numerical simulation) in physics and how would you implement it? Can it be simulated by a high potential, low negative potential at the boundaries, how?

Or an imaginary (damping) potential? It has to do with this sentence if found in arXiv:083.0507 (last paragraph of page 5):

...but an absorbing region far from the horizon is required to prevent the onset of spurious dynamical instabilities due to excitations circulating around the integration box.

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  • $\begingroup$ @KyleKanos: as you are interested in this problem, please answer it $\endgroup$
    – MrQ
    Commented Feb 12, 2022 at 14:04
  • $\begingroup$ My experience in Comp-Phys is with fluid dynamics, not QM; in that case, absorbing BCs are usually $\partial_xu=0$. Whether that holds for the GPE the authors are intending to solve, I do not know. $\endgroup$
    – Kyle Kanos
    Commented Feb 12, 2022 at 14:13
  • $\begingroup$ @KyleKanos: I mean with potentials. High potentials at the edges mean reflecting walls. And so forth... Could you maybe upvote this question such that it gets an answer faster. This is a bit in general not only QM $\endgroup$
    – MrQ
    Commented Feb 12, 2022 at 14:14
  • $\begingroup$ In quantum mechanics an imaginary part in the potential corresponds to decay that's possible in that region. Note, that this makes the time evolution non-unitary (and this is correct, the probability of finding the particle anywhere goes down with time!). It can be understood as an approximation for weak coupling to a many mode environment and tracing the environment out. A perfectly absorbing wall is, however, more difficult (just cranking the absorption up will lead to reflection). $\endgroup$
    – Sebastian Riese
    Commented Feb 12, 2022 at 14:44
  • $\begingroup$ @SebastianRiese: how would you do it than for this problem, numerically (e.g., in a computer program)? How would you change the potential? $\endgroup$
    – MrQ
    Commented Feb 12, 2022 at 14:46

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