The MS Unidirectional Current as a Generalization of the ABC Absorption Current
Abstract
For a free scalar particle in one spatial dimension, in a single-pass half-line geometry, we compare the absorbing Robin boundary condition with the generalized Marchewka--Schuss (MS) unidirectional-current family. Robin absorption is characterized by a single parameter κ>0: once κ is specified, its momentum-dependent absorption profile is fixed. In the generalized MS construction, by contrast, the detector response is described by a spectral function λ(k), subject to the positivity and subnormalization conditions of the detection law. We show that every Robin choice of κ corresponds to the particular MS calibration λκ(k)=πκ/(k+κ)2, which reproduces the complete Robin absorption current for every admissible one-sided spectral amplitude and at every time. Thus the entire one-parameter Robin absorption family is contained within the generalized MS family. The MS construction is more general: the choice λfull(k)=π/(4k) gives unit absorption efficiency for every wave number, which cannot be achieved by any fixed Robin parameter. In this precise sense, the generalized MS detector process extends the Robin absorbing-boundary family. We also compare their asymptotic behavior in the ballistic fixed-ray regime and in the fixed-distance late-time limit.
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BibTeX
@misc{marchewka2026unidirectional,
title = {{The MS Unidirectional Current as a Generalization of the ABC Absorption Current}},
author = {Avi Marchewka},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29969},
eprint = {2608.29969},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29969},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The MS Unidirectional Current as a Generalization of the ABC Absorption Current
AU - Avi Marchewka
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29969
UR - https://arxiv.org/abs/2608.29969
AB - For a free scalar particle in one spatial dimension, in a single-pass half-line geometry, we compare the absorbing Robin boundary condition with the generalized Marchewka--Schuss (MS) unidirectional-current family. Robin absorption is characterized by a single parameter κ>0: once κ is specified, its momentum-dependent absorption profile is fixed. In the generalized MS construction, by contrast, the detector response is described by a spectral function λ(k), subject to the positivity and subnormalization conditions of the detection law. We show that every Robin choice of κ corresponds to the particular MS calibration λ_κ(k)=πκ/(k+κ)^2, which reproduces the complete Robin absorption current for every admissible one-sided spectral amplitude and at every time. Thus the entire one-parameter Robin absorption family is contained within the generalized MS family. The MS construction is more general: the choice λ_full(k)=π/(4k) gives unit absorption efficiency for every wave number, which cannot be achieved by any fixed Robin parameter. In this precise sense, the generalized MS detector process extends the Robin absorbing-boundary family. We also compare their asymptotic behavior in the ballistic fixed-ray regime and in the fixed-distance late-time limit.
ER -