Real discrete spectrum of complex PT-symmetric scattering potentials

Abstract

We investigate the parametric evolution of the real discrete spectrum of several complex PT symmetric scattering potentials of the type $V(x)=-V_1{F}_e(x)+i{V}_2{F}_o(x),V_1>0,F_e(x)>0$ by varying $V_2$ slowly. Here $e,o$ stand for even and odd parity and $F_{e,o}(\pm \infty )=0$. Unlike the case of Scarf II potential, we find a general absence of the recently explored accidental (real to real) crossings of eigenvalues in these scattering potentials. On the other hand, we find a general presence of coalescing of real pairs of eigenvalues to the complex conjugate pairs at a finite number of exceptional points. We attribute such coalescings of eigenvalues to the presence of a finite barrier (on the either side of $x=0$ ) which has been linked to a recent study of stokes phenomenon in the complex PT-symmetric potentials.

13 pages and 6 Figures

References in corpus (1)

• Accidental crossings of eigenvalues in one-dimensional complex PT-symmetric Scarf-II potential

Cited by in corpus (2)

• Three types of discrete energy eigenvalues in complex PT-symmetric scattering potentials
• Dirichlet spectrum of the paradigm model of complex PT-symmetric potential: $V(x)=-(ix{)}^N$