Document Type : Research
Authors
1 Department of Physics, Faculty of Sciences Shahid Bahonar University of Kerman, Kerman, Iran
2 Department of Physics, Faculty of Sciences, Research and Technology Institute of Plant Production, Afzalipour Research Institute, Shahid Bahonar University of Kerman, Kerman Iran
Abstract
In this paper, the spectral behavior of the Dunkl-derivative-based
harmonic oscillator in the presence of a PT-symmetric non-
Hermitian potential is studied. By applying a balanced gain–loss
profile in the form of iγx , the Dunkl–Schrödinger equation is
solved numerically, and the influence of the Dunkl reflection
parameter μμ on the real-phase stability is investigated. The results
demonstrate that increasing μμ monotonically lowers the PT-
symmetry breaking threshold, thereby playing a destabilizing role in
the spectral response of the system. This behavior is fully observed in
the real spectrum, mode splitting, and the emergence of imaginary
eigenvalues after the exceptional point (EP).
A detailed numerical convergence analysis, along with an
examination of eigenvalue and eigenvector condensation, confirms
that the computed exceptional points are mathematically valid and do
not arise from numerical instabilities. Furthermore, using wave
packet time evolution, the combined effect of the Dunkl parameter
and gain–loss on the dynamics of optical propagation is illustrated.
An empirical trend for the PT-threshold dependence on μμ is
proposed, showing a better fit to a square-root law than to a linear
model.
These results provide a clear picture of the role of the Dunkl operator
in non-reciprocal optics and may serve as a starting point for
designing optical structures with reflective defects or nonlocal
behaviors.
Keywords
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