Volume 101, Number 1, January 2013
|Number of page(s)||6|
|Section||The Physics of Elementary Particles and Fields|
|Published online||08 January 2013|
-symmetric lattices with spatially extended gain/loss are generically unstable
1 Department of Mathematics, McMaster University - Hamilton, Ontario, Canada, L8S 4K1
2 Department of Mathematics and Statistics, University of Massachusetts - Amherst, MA 01003-9305, USA
3 Department of Physics, University of Athens - Panepistimiopolis, Zografos, Athens 157 84, Greece, EU
Received: 2 November 2012
Accepted: 6 December 2012
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 real for localized or compact -symmetric potentials. The linear lattices are analyzed through discrete Fourier transform techniques complemented by numerical computations.
PACS: 11.30.Er – Charge conjugation, parity, time reversal, and other discrete symmetries / 42.25.-p – Wave optics / 42.82.Et – Waveguides, couplers, and arrays
© EPLA, 2013
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