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D.E. Pelinovsky, P.G. Kevrekidis, and D.J. Frantzeskakis,

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PT-symmetric Lattices with extended gain/loss are generically unstable

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European Physics Letters 101 (2013) 11002 (6 pages)

**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 nonzero
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.

**Keywords:**

PT-symmetry, discrete Schrodinger equation, eigenvalues, discrete Fourier transforms