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Inflow boundary conditions and nonphysical solutions to the Wigner transport equation

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Abstract

We investigate the emergence of nonphysical solutions to the steady-state Wigner transport equation on finite-sized simulation domains with inflow boundary conditions. We find that inflow boundary conditions are generally valid, but the wave number uncertainty of injected wave packets has a lower bound that can be significantly higher than usually assumed. Large values of the so-called quantum evolution term (which captures spatial nonlocality in the Wigner transport equation) near simulation-domain boundaries are the cause of spurious reflections, the often-reported discontinuity of the Wigner function at zero wave vector, and negative probabilities. We offer a simple relationship between the lower bound of the wave number uncertainty and simulation parameters that will ensure physical results with inflow boundary conditions.

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Data will be made available upon reasonable request.

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Acknowledgements

This work was funded by DOE-BES, award DE-SC0008712 (S.S. and O.J.), and by UW-Madison through WARF/Fall Competition (M.K.E.) and the Splinter Professorship (I.K.). The authors gratefully acknowledge the compute resources and assistance of the UW-Madison Center for High Throughput Computing in the Department of Computer Sciences.

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  1. Department of Electrical and Computer Engineering, University of Wisconsin-Madison, 1415 Engineering Dr., Madison, Wisconsin, 53706, USA

    M. K. Eryilmaz, S. Soleimanikahnoj, O. Jonasson & I. Knezevic

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  1. M. K. Eryilmaz
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  2. S. Soleimanikahnoj
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  3. O. Jonasson
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  4. I. Knezevic
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Correspondence to I. Knezevic.

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Eryilmaz, M.K., Soleimanikahnoj, S., Jonasson, O. et al. Inflow boundary conditions and nonphysical solutions to the Wigner transport equation. J Comput Electron 20, 2039–2051 (2021). https://doi.org/10.1007/s10825-021-01793-6

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