Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2007-11-29
Phys. Rev. A 77, 013618 (2008)
Nonlinear Sciences
Chaotic Dynamics
9 pages, 6 figures
Scientific paper
10.1103/PhysRevA.77.013618
The extended Gross-Pitaevskii equation for the Bose-Einstein condensation of gases with attractive 1/r-interaction has a second solution which is born together with the ground state in a tangent bifurcation. At the bifurcation point both states coalesce, i.e., the energies and the wave functions are identical. We investigate the bifurcation point in the context of exceptional points, a phenomenon known for linear non-Hermitian Hamiltonians. We point out that the mean field energy, the chemical potential, and the wave functions show the same behavior as an exceptional point in a linear, non-symmetric system. The analysis of the analytically continued Gross-Pitaevskii equation reveals complex waves at negative scattering lengths below the tangent bifurcation. These solutions are interpreted as a decay of the condensate caused by an absorbing potential.
Cartarius Holger
Main Jörg
Wunner Günter
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