Complex periodic potentials with real band spectra

This paper demonstrates that complex PT-symmetric periodic potentials posse ss real band spectra. However, there are significant qualitative difference s in the band structure for these potentials when compared with conventiona l real periodic potentials. For example, while the potentials V (x) = i sin (2N+1) (x) (N = 0, 1,2,...) have infinitely many gaps, at the band edges th ere are periodic wave functions but no antiperiodic wave functions. Numeric al analysis and higher-order WKB techniques are used to establish these res ults. (C) 1999 Elsevier Science B.V.