Variational treatment for a complex PT-potential

Avinash Khare, Bhabani Prasad Mandal

Bruce Cameron Reed

GÉZA LÉVAI, F. Cannata, Alberto Ventura

We study a particular solvable potential and analyse the effect of 𝒫𝒯 symmetry on its bound state as well as scattering solutions. We determine the transmission and reflection coefficients for the 𝒫𝒯-symmetric case and also formulate the problem in terms of an SU (1,1) potential group, which allows unified treatment of the discrete and the continuous spectra in a natural way. We find that (bound and scattering) states of the 𝒫𝒯-symmetric problem supply a basis for the unitary irreducible representations of the SU (1,1) potential group, and this gives a straightforward group theoretical interpretation of the fact that the (complex) 𝒫𝒯-invariant potential has a real energy spectrum.

Stefan Weigert

Lini Devassy, Chandroth P. Jisha, Alessandro Alberucci +1 more

Dynamics and properties of nonlinear matter waves in a trapped BEC subject to a PT-symmetric linear potential, with the trap in the form of a super-Gaussian potential, are investigated via a variational approach accounting for the complex nature of the soliton. In the process, we address how the shape of the imaginary part of the potential, that is, a gain-loss mechanism, affects the self-localization and the stability of the condensate. Variational results are found to be in good agreement with full numerical simulations for predicting the shape, width, and chemical potential of the condensate until the PT breaking point. Variational computation also predicts the existence of solitary solution only above a threshold in the particle number as the gain-loss is increased, in agreement with numerical simulations.

Zafar Ahmed, D. C. Ghosh, Joseph Amal Nathan