English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We propose a new normalized Sobolev gradient flow for the Gross-Pitaevskiieigenvalue problem based on an energy inner product that depends on timethrough the density of the flow itself. The gradient flow is well-defined andconverges to an eigenfunction. For ground states we can quantify theconvergence speed as exponentially fast where the rate depends on spectral gapsof a linearized operator. The forward Euler time discretization of the flowyields a numerical method which generalizes the inverse iteration for thenonlinear eigenvalue problem. For sufficiently small time steps, the methodreduces the energy in every step and converges globally in $H^1$ to aneigenfunction. In particular, for any nonnegative starting value, the groundstate is obtained. A series of numerical experiments demonstrates thecomputational efficiency of the method and its competitiveness with establisheddiscretizations arising from other gradient flows for this problem.

Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem: global convergence and computational efficiency