Zafar Ahmed
Articles written in Pramana – Journal of Physics
Volume 54 Issue 3 March 2000 pp 413-422 Research Articles
Random matrix model for disordered conductors
We present a random matrix ensemble where real, positive semi-definite matrix elements,
Volume 73 Issue 2 August 2009 pp 323-328
Scarcity of real discrete eigenvalues in non-analytic complex $\mathcal{PT}$-symmetric potentials
We find that a non-differentiability occurring whether in real or imaginary part of a complex $\mathcal{PT}$-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 $\mathcal{PT}$ -symmetric potentials $ix|x|$ and $ix$, respectively.
Volume 95 All articles Published: 16 April 2021 Article ID 0063 Reserach Article
The versatile and exactly solvable Scarf II potential has been predicting, confirming and demonstrating interesting phenomena in complex PT-symmetric sector, most impressively. However, for the non-PT-symmetric sector, it has gone underutilised. Here, we present the most simple analytic forms for the scattering coefficients $(T (k), R(k), | det S(k)|)$. On the one hand, these forms demonstrate earlier effects and confirm the recent ones. On the other hand, they make new predictions – all simple and analytical. We show the possibilities of both self-dual and non-self-dual spectral singularities (NSDSS) in two non-PT sectors (potentials). The former one is not accompanied by time-reversed coherent perfect absorption (CPA) and gives rise to the parametrically controlled splitting of spectral singularity (SS) into a finite number of complex conjugate pairs of eigenvalues (CCPEs). NSDSS behave just oppositely: CPA but no splitting of SS. We demonstrate a one-sided reflectionlessness without invisibility. Most importantly, we bring out a surprising coexistence of both real discrete spectrum and a single SS in a fixed potential. Nevertheless, so far, the complex Scarf II potential is not known to be pseudo-Hermitian ($η ^{−1}Hη = H^{†})$ under a metric of the type $η(x)$.
Volume 96 All articles Published: 26 July 2022 Article ID 0144 Research Article
PT-symmetric potentials with imaginary asymptotic saturation
ZAFAR AHMED SACHIN KUMAR JOSEPH AMAL NATHAN
We point out that PT-symmetric potentials
Volume 96, 2022
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