多连通截面波导结构：复Robin参数外场中传播的演化
Guiding structures with multiply connected cross-sections: evolution of propagation in external fields at complex Robin parameters
摘要：
假设内外壁Robin边界条件分别包含外推长度$Λ_{in}$和$Λ_{out}$，在标量Helmholtz方程的框架内，分析了二维环形和三维无限长单位宽度内径$ρ_0$直波导在纵向均匀磁场$\bf B$和Aharonov-Bohm磁通叠加时的特性，虚部不为零结果表明，相比，磁盘的几何形状，环开辟了额外的可能性，通过调整虚拟组件的罗宾参数在每个限制圆周上的磁化强度和电流;特别是，恢复一个无损的纵向磁通量的可能性归零虚部$E_i$的总横向能量$E$进行了讨论。能量$E$在具有相反符号的$Λ_{in}$和$Λ_{out}$的虚部之间的特殊相关下变为实的，这在物理上对应于通过环的内部和外部界面的相等横向通量。在非常大的半径的渐近情况下，简单的表达式推导出并应用于分析的真实能量$E$对$Λ_{in}$和$Λ_{out}$的依赖性。在磁场影响中也出现了新的特征;例如，如果对于量子盘，虚能量$E_i$被强强度$B$猝灭，那么对于环，这只有在内部罗宾距离$Λ_{in}$为实数时才发生;否则，它几乎二次依赖于$B$，并相应地增强了反应性散射。密切相关的问题，否则均匀介质中的孔也解决了实际和复杂的外推长度的比较分析，其点对应的重点。
英文摘要：
Properties of the two-dimensional ring and three-dimensional infinitely long straight hollow waveguide with unit width and inner radius $ρ_0$ in the superposition of the longitudinal uniform magnetic field $\bf B$ and Aharonov-Bohm flux are analyzed within the framework of the scalar Helmholtz equation under the assumption that the Robin boundary conditions at the inner and outer confining walls contain extrapolation lengths $Λ_{in}$ and $Λ_{out}$, respectively, with nonzero imaginary parts. It is shown that, compared to the disk geometry, the annulus opens up additional possibilities of varying magnetization and currents by tuning imaginary components of the Robin parameters on each confining circumference; in particular, the possibility of restoring a lossless longitudinal flux by zeroing imaginary part $E_i$ of the total transverse energy $E$ is discussed. The energy $E$ turns real under special correlation between the imaginary parts of $Λ_{in}$ and $Λ_{out}$ with the opposite signs what physically corresponds to the equal transverse fluxes through the inner and outer interfaces of the annulus. In the asymptotic case of the very large radius, simple expressions are derived and applied to the analysis of the dependence of the real energy $E$ on $Λ_{in}$ and $Λ_{out}$. New features also emerge in the magnetic field influence; for example, if, for the quantum disk, the imaginary energy $E_i$ is quenched by the strong intensities $B$, then for the annulus this takes place only when the inner Robin distance $Λ_{in}$ is real; otherwise, it almost quadratically depends on $B$ with the corresponding enhancement of the reactive scattering. Closely related problem of the hole in the otherwise uniform medium is also addressed for real and complex extrapolation lengths with the emphasis on the comparative analysis with its dot counterpart.
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