Darmstadt 2008 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 37: Quantengase (Wechselwirkungseffekte I)

Q 37.6: Talk

Thursday, March 13, 2008, 12:15–12:30, 1C

Linear stability of Bose-Einstein condensates with attractive 1/r-interaction — •Jörg Main, Holger Cartarius, Tomaž Fabčič, and Günter Wunner — 1. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart

We investigate the stability of the two nodeless stationary solutions, which are created in a tangent bifurcation in the Gross-Pitaevskii equation for condensates with attractive 1/r-interaction. Using the Fréchet derivative of the time-dependent nonlinear integro-differential equation, we calculate the eigenvalues of the linearized system. The two stationary solutions are found to be an elliptic and a hyperbolic fixed point. The numerically exact solutions are compared with the results of an approximative variational approach, which leads to analytic expressions for the eigenmodes of the linearized time-dependent equation. There are quantitative differences between both approaches, however, qualitatively they agree very well.