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

We illustrate, through a series of prototypical examples, that linear parity-time () symmetric lattices with spatially extended gain/loss 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 piecewise constant or linear imaginary potentials. On the other hand, this instability can be avoided and the spectrum can be …