PT-symmetric lattices with spatially extended gain/loss are generically unstable

TL;DR

This paper demonstrates that linear PT-symmetric lattices with extended gain/loss profiles are generally unstable for any non-zero gain/loss coefficient, contrasting with the stability possible in localized or compact PT-symmetric potentials.

Contribution

It provides a systematic analysis showing the inherent instability of extended gain/loss PT-symmetric lattices and identifies conditions under which stability can be achieved.

Findings

Extended gain/loss profiles lead to instability in PT lattices.

Localized or compact PT potentials can have real spectra and stability.

Fourier analysis and numerical methods support the instability results.

Abstract

We illustrate, through a series of prototypical examples, that linear parity-time (PT) symmetric lattices with extended gain/loss profiles are generically unstable, for any non-zero value of the gain/loss coefficient. Our examples include a parabolic real potential with a linear imaginary part and the cases of no real and constant or linear imaginary potentials. On the other hand, this instability can be avoided and the spectrum can be real for localized or compact PT-symmetric potentials. The linear lattices are analyzed through discrete Fourier transform techniques complemented by numerical computations.