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arXiv · 0711.4786

Discovery of exceptional points in the Bose-Einstein condensation of gases with attractive 1/r-interaction

Holger Cartarius·Jörg Main·Günter Wunner
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Abstract

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.

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Holger Cartarius, Jörg Main, Günter Wunner. 2007-11-29. Discovery of exceptional points in the Bose-Einstein condensation of gases with attractive 1/r-interaction. https://doi.org/10.1103/physreva.77.013618

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