Tag P. K. Panigrahi

From particle in a box to PT -symmetric systems via isospectral deformation

Philip Cherian, Kumar Abhinav, P. K. Panigrahi

A family of PT -symmetric complex potentials are obtained which is isospectral to free particle in an infinite complex box in one dimension (1-D). These are generalizations to the cosec2(x) potential, isospectral to particle in a real infinite box. In the complex plane, the infinite box is extended parallel to the real axis having a real width, which is found to be an integral multiple of a constant quantum factor, arising due to boundary conditions necessary for maintaining the PT -symmetry of the superpartner. As the spectra of the particle in a box is still real, it necessarily picks out the unbroken PT -sector of its superpartner, thereby invoking a close relation between PT -symmetry and SUSY for this case.

Mathematical Physics (math-ph); Quantum Physics (quant-ph)

Conserved Correlation in PT -symmetric Systems: Scattering and Bound States

Kumar Abhinav, Arun Jayannavar, P. K. Panigrahi

For one-dimensional PT -symmetric systems, it is observed that the non-local product obtained from the continuity equation can be interpreted as a conserved corre- lation function. This leads to physical conclusions, regarding both discrete and continuum states of such systems. Asymptotic states are shown to have necessarily broken PT -symmetry, leading to modified scattering and transfer matrices. This yields restricted boundary conditions, e.g., in- cidence from both sides, analogous to that of the proposed PT CPA laser. The interpretation of left and right states leads to a Hermitian S-matrix, resulting in the non-conservation of the flux. This further satisfies a duality condition, identical to the optical analogues. However, the non-local conserved scalar implements alternate boundary conditions in terms of in and out states, leading to the pseudo-Hermiticity condition in terms of the scattering matrix. Interestingly, when PT -symmetry is preserved, it leads to stationary states with real energy, naturally inter- pretable as bound states. The broken PT -symmetric phase is also captured by this correlation, with complex-conjugate pair of energies, interpreted as resonances.

Quantum Physics (quant-ph)