A minimisation approach for computing the ground state of Gross-Pitaevskii systems

Authors:
Marco Caliari;Alexander Ostermann;Stefan Rainer;Mechthild Thalhammer
Affiliations:
Dipartimento di Informatica, Universití degli Studi di Verona, Ca' Vignal 2, Strada Le Grazie 15, I-37134 Verona, Italy;Institut für Mathematik, Leopold-Franzens Universität Innsbruck, Technikerstraíe 13/7, A-6020 Innsbruck, Austria;Institut für Mathematik, Leopold-Franzens Universität Innsbruck, Technikerstraíe 13/7, A-6020 Innsbruck, Austria;Institut für Mathematik, Leopold-Franzens Universität Innsbruck, Technikerstraíe 13/7, A-6020 Innsbruck, Austria
Venue:
Journal of Computational Physics
Year:
2009

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Abstract

In this paper, we present a minimisation method for computing the ground state of systems of coupled Gross-Pitaevskii equations. Our approach relies on a spectral decomposition of the solution into Hermite basis functions. Inserting the spectral representation into the energy functional yields a constrained nonlinear minimisation problem for the coefficients. For its numerical solution, we employ a Newton-like method with an approximate line-search strategy. We analyse this method and prove global convergence. Appropriate starting values for the minimisation process are determined by a standard continuation strategy. Numerical examples with two- and three-component two-dimensional condensates are included. These experiments demonstrate the reliability of our method and nicely illustrate the effect of phase segregation.