We derive a continuity equation to study transport properties in a ##IMG## [http://ej.iop.org/images/1751-8121/53/44/445308/aabb513ieqn2.gif] {$\mathcal{P}\mathcal{T}$} -symmetric tight-binding chain with gain and loss in symmetric configurations. This allows us to identify the density fluxes in the system, and to define a transport coefficient to characterize the efficiency of transport of each state. These quantities are studied explicitly using analytical expressions for the eigenvalues and eigenvectors of the system. We find that in states with broken ##IMG## [http://ej.iop.org/images/1751-8121/53/44/445308/aabb513ieqn3.gif] {$\mathcal{P}\mathcal{T}$} -symmetry, transport is inefficient, in the sense that either inflow exceeds outflow and density accumulates within the system, or outflow exceeds inflow, and the system becomes depleted. We also report the appearance of two subsets of interesting eigenstates whose eigenvalues are indep...

中文翻译：

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## IMG ##的光谱和传输性质[http://ej.iop.org/images/1751-8121/53/44/445308/toc_aabb51​​3ieqn1.gif] {$ \ mathcal {P} \ mathcal {T} $}具有收益和损失的对称紧缚链

我们导出一个连续性方程来研究## IMG ## [http://ej.iop.org/images/1751-8121/53/44/445308/aabb51​​3ieqn2.gif] {$ \ mathcal {P} \ mathcal {T} $}-对称紧密绑定链，在对称配置中具有增益和损耗。这使我们能够识别系统中的密度通量，并定义传输系数来表征每种状态的传输效率。使用系统的特征值和特征向量的解析表达式来明确研究这些量。我们发现在## IMG ##损坏的州[http://ej.iop.org/images/1751-8121/53/44/445308/aabb51​​3ieqn3.gif] {$ \ mathcal {P} \ mathcal {T } $}-对称，传输效率低下，从某种意义上说，要么流入超过流出并且系统内积累了密度，要么流出超过流入而系统耗尽了。