局部有限自由空间作为PT-对称介质的极限情形
Locally finite free space as limiting case of PT-symmetric medium
摘要：
本文明确地证明了由等厚势系“$+iV$”和“$-iV$”的$N$单元组成的定长有限层状$PT$ -对称系统的传递矩阵在极限$N \rightarrow \infty$中成为单位矩阵。这个结果对于任意波矢$k$的波都是正确的。这表明，在该极限下，对于穿过该长度$L$的所有波，透射系数总是1，而反射振幅为零。因此，有限长$L$的自由空间可以表示为$PT$对称介质。
英文摘要：
We explicitly prove that the transfer matrix of a finite layered $PT$-symmetric system of fix length $L$ consisting of $N$ units of the potential system `$+iV$' and `$-iV$' of equal thickness becomes a unit matrix in the limit $N \rightarrow \infty$. This result is true for waves of arbitrary wave vector $k$. This shows that in this limit, the transmission coefficient is always unity while the reflection amplitude is zero for all waves traversing this length $L$. Therefore, a free space of finite length $L$ can be represented as a $PT$-symmetric medium.
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