Scarcity of real discrete eigenvalues in non-analytic complex PT mathcal{P}mathcal{T} -symmetric potentials

摘要

We find that a non-differentiability occurring whether in real or imaginary part of a complex -symmetric potential causes a scarcity of the real discrete eigenvalues despite the real part alone possessing an infinite spectrum. We demonstrate this by perturbing the real potentials x 2 and |x| by imaginary -symmetric potentials ix/it|x| and ix, respectively.