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arXiv · 2201.00010

Locally finite free space as limiting case of PT-symmetric medium

Mohammad Hasan·Mohammad Umar·Bhabani Prasad Mandal
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Abstract

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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Mohammad Hasan, Mohammad Umar, Bhabani Prasad Mandal. 2021-12-30. Locally finite free space as limiting case of PT-symmetric medium. https://arxiv.org/abs/2201.00010

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