Reciprocity and unitarity in scattering from a non-Hermitian complex PT-symmetric potential

Abstract

In quantum scattering, Hermiticity is necessary for both reciprocity and unitarity. Reciprocity means that both reflectivity (R) and transmitivity (T) are insensitive to the direction of incidence of a wave (particle) at a scatterer from left/right. Unitarity means that R+T=1. In scattering from non-Hermitian PT-symmetric structures the (left/right) handedness (non-reciprocity) of reflectivity is known to be essential and unitarity remains elusive so far. Here we present a surprising occurrence of both reciprocity and unitarity in scattering from a complex PT-symmetric potential. In special cases, we show that this potential can even become invisible (R=0, T=1) from both left and right sides. We also find that this potential in a parametric regime enjoys a pseudo-unitarity of the type $T+\sqrt{R_{left}{R}_{right}}=1$.

7 pages. no figures and no tables, two corrections, appeared in Phys. Lett. A

References in corpus (2)

• Spectral singularity and deep multiple minima in the reflectivity in non-Hermitian (complex) Ginocchio potential
• Classical Trajectories of the Continuum States of the $\mathcal{P}\mathcal{T}$ symmetric Scarf II potential

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• Scattering properties of anti-parity-time symmetric non-Hermitian system
• Scattering amplitudes for the rationally extended P T symmetric complex potentials
• Spectral Singularity in confined PT symmetric optical potential
• A unidirectional invisible PT-symmetric complex crystal with arbitrary thickness
• Coherent perfect absorption with and without lasing in complex potentials
• Unitary Scattering Protected by Pseudo-Hermiticity
• Helical resonant transport and purified amplification at an exceptional point
• Analytical solutions for the radial Scarf II potential
• Transmission across non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric quantum dots and ladders
• Three types of discrete energy eigenvalues in complex PT-symmetric scattering potentials
• Scattering of Spin-$\frac{1}{2}$ Particles from a $\mathcal{P}\mathcal{T}$-symmetric Complex Potential
• Scattering in a varying mass PT symmetric double heterojunction
• Reciprocity in parity violating non-Hermitian systems