AI 中文总结
该研究将Robin边界条件与广义MS单向电流族对比，证明Robin族包含于MS族，且MS族可实现Robin族无法达到的全波数单位吸收效率，扩展了吸收边界族。
AI 中文摘要
对于一维空间中处于单程半直线几何结构下的自由标量粒子，我们将吸收型Robin边界条件与广义Marchewka-Schuss（MS）单向电流族进行对比。Robin吸收由单个参数κ>0表征：一旦κ被确定，其依赖于动量的吸收分布便固定下来。相比之下，在广义MS构造中，探测器响应由满足探测定律的正性和次归一化条件的谱函数λ(k)描述。我们证明，每一个Robin参数κ的选择都对应着特定的MS校准λ_κ(k)=πκ/(k+κ)²，该校准可在所有允许的单侧谱振幅及任意时刻重现完整的Robin吸收电流。因此，整个单参数Robin吸收族都包含在广义MS族中。MS构造更具一般性：选择λ_full(k)=π/(4k)可使所有波数的吸收效率达到1，而这是任何固定Robin参数都无法实现的。在这一精确意义上，广义MS探测器过程扩展了Robin吸收边界族。我们还对比了二者在弹道固定射线区域及固定距离晚时极限下的渐近行为。
英文摘要
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 $λ_{\rm full}(k)=π/(4k)$ 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.
Comments8 pages
