Solvable PT-symmetric model with a tunable interspersion of nonmerging levels -: art. no. 062109

We study the spectrum in such a PT-symmetric square well (of a diameter L <=infinity) where the "strength of the non-Hermiticity" is controlled by the two parameters, viz., by an imaginary coupling ig and by the distance l < L of its onset from the origin. We solve this problem and confirm that the spectrum is discrete and real in a nonempty interval of g <= g(0)(l,L). Surprisingly, a specific distinction between the bound states is found in their asymptotic stability/instability with respect to an unlimited growth of g beyond g(0)(l,L). In our model, all of the low-lying levels remain asymptotically unstable at the small l < L and finite L while only the stable levels survive near l approximate to L <infinity or in the purely imaginary force limit with 0 < l < L=infinity. In between these two extremes, an unusual and tunable, variable pattern of the interspersed "robust" and "fragile" subspectra of the real levels is obtained. (C) 2005 American Institute of Physics.