Z. Naturforsch. **68a,** 587 – 598
(2013)

doi:10.5560/ZNA.2013-0049

Exotic Resonant States for One-Dimensional Twin Complex Square Potentials

Cornelia
Grama,
Nicolae
Grama, and
Ioan
Zamfirescu

Horia Hulubei National Institute for Physics and Nuclear Engineering, Bucharest,
P.O. Box MG-6, Romania

Received February 12, 2013 / published online August 21, 2013

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.

*Key words:* Tunnelling; Natural Modes; Traversal Time; Scattering Theory.