TY - JOUR AU - Wunner, G. AU - Cartarius, H. AU - Koeberle, P. AU - Main, J. AU - Rau, S. PY - 2011/01/04 Y2 - 2024/03/28 TI - Exceptional Points for Nonlinear Schroedinger Equations Describing Bose-Einstein Condensates of Ultracold Atomic Gases JF - Acta Polytechnica JA - Acta Polytech VL - 51 IS - 4 SE - Articles DO - 10.14311/1418 UR - https://ojs.cvut.cz/ojs/index.php/ap/article/view/1418 SP - AB - The coalescence of two eigenfunctions with the same energy eigenvalue is not possible in Hermitian Hamiltonians. It is, however, a phenomenon well known from non-hermitian quantum mechanics. It can appear, e.g., for resonances in open systems, with complex energy eigenvalues. If two eigenvalues of a quantum mechanical system which depends on two or more parameters pass through such a branch point singularity at a critical set of parameters, the point in the parameter space is called an exceptional point. We will demonstrate that exceptional points occur not only for non-hermitean Hamiltonians but also in the nonlinear Schroedinger equations which describe Bose-Einstein condensates, i.e., the Gross-Pitaevskii equation for condensates with a short-range contact interaction, and with additional long-range interactions. Typically, in these condensates the exceptional points are also found to be bifurcation points in parameter space. For condensates with a gravity-like interaction between the atoms, these findings can be confirmed in an analytical way. ER -