Exotic Resonant States for One-Dimensional Twin Complex Square Potentials

The natural modes for one-dimensional (1D) twin square potentials of complex strength g are studied. A global analysis of the natural modes based on the construction of the Riemann surfaces R_g^I and R_g^II of the multiple valued function k = k(g), where k(g) defines the poles of the transmission coefficient, is done. To each nonradiative or radiative mode a sheet of the Riemann surface is associated. All the natural modes of the system are identified and treated in a unified way. New classes of resonant state poles with exotic properties are identified on the k-plane images of the sheets of R_g^I and R_g^II and the properties of the exotic modes are studied. The traversal time through the 1D twin square potentials is analysed. Subluminal and superluminal traversal times are evidenced. An approximate formula for the frequencies k for which the maximal superluminal velocities are gained as a function of the potential parameters is given.