PT-symmetry in one-dimensional quantum periodic potentials

A complete band structure is shown to exist for one-dimensional periodic non-Hermitian potentials exhibiting PT-symmetry. The full band spectrum is exactly given and some of its properties discussed, specially those concerning the role of the imaginary parameters of the couplings. Infinite periodic arrays constructed with finite chains each one made of N different ultralocal couplings are used as models of this one-dimensional complex quantum wire. (C) 2003 Elsevier B.V. All rights reserved.