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Quantum Simulation

Real discrete spectrum of complex PT-symmetric scattering potentials

arXiv
Authors: Zafar Ahmed, Joseph Amal Nathan, Dhruv Sharma, Dona Ghosh

Year

2015

Paper ID

26581

Status

Preprint

Abstract Read

~2 min

Abstract Words

144

Citations

N/A

Abstract

We investigate the parametric evolution of the real discrete spectrum of several complex PT symmetric scattering potentials of the type V(x)=-V1 Fe(x) + i V2 Fo(x), V1>0, Fe(x)>0 by varying V2 slowly. Here e,o stand for even and odd parity and Fe,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.

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  • We investigate the parametric evolution of the real discrete spectrum of several complex PT symmetric scattering potentials of the type V(x)=-V1 Fe(x) + i V2 Fo(x), V1>0...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1510.06226 [2] arXiv https://arxiv.org/abs/1510.06226 [3] Publisher https://arxiv.org/abs/1510.06226

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