Locally finite free space as limiting case of PTsymmetric medium
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.
 Publication:

arXiv eprints
 Pub Date:
 December 2021
 arXiv:
 arXiv:2201.00010
 Bibcode:
 2022arXiv220100010H
 Keywords:

 Quantum Physics;
 High Energy Physics  Theory
 EPrint:
 9 pages, 3 figs, Latex