2014/10/31 by Nikolas Abt, Holger Cartarius, G眉nter Wunner
Physics and Astronomy 路 #Cold Atom Physics and Bose-Einstein Condensates #Eigenvalues and eigenvectors #Formalism (music) #Instability #Nonlinear system #Pulsars and Gravitational Waves Research #Quantum Mechanics and Non-Hermitian Physics #Supersymmetric quantum mechanics #Supersymmetry #cond-mat.quant-gas #quant-ph
paper 路 pdf 路 doi:10.1007/s10773-014-2467-0
published as Int. J. Theor. Phys. 54, 4054 (2015) 路 16 pages, 10 figures, minor corrections in the text and equations
arxiv created 2014/12/24 路 openalex publication_date 2015/01/29 路 arxiv updated 2015/10/16 路 openalex created_date 2016/06/24 路 openalex updated_date 2026/08/05
The most important properties of a Bose-Einstein condensate subject to balanced gain and loss can be modelled by a Gross-Pitaevskii equation with an external PT-symmetric double-delta potential. We study its linear variant with a supersymmetric extension. It is shown that both in the PT-symmetric as well as in the PT-broken phase arbitrary stationary states can be removed in a supersymmetric partner potential without changing the energy eigenvalues of the other state. The characteristic structure of the singular delta potential in the supersymmetry formalism is discussed, and the applicability of the formalism to the nonlinear Gross-Pitaevskii equation is analysed. In the latter case the formalism could be used to remove PT-broken states introducing an instability to the stationary PT-symmetric states.