Wave Functions and Their Densities in Metric Space

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• Prof Irene d'Amico, U of York
• Thursday 23 February 2012, 13:45-15:00
• Theory Library.

If you have a question about this talk, please contact Dr Dimitri M Gangardt.

Hilbert space combines the properties of two different types of mathematical spaces: vector space and metric space. While the vector-space aspects are widely used, the metric-space aspects are much less exploited. Here¹ we show that a suitable metric stratifies Fock space into concentric spheres on which maximum and minimum distances between states can be defined and geometrically interpreted. Unlike the usual Hilbert-space analysis, our results apply also to the reduced space of only ground states and to that of particle densities, which are metric, but not Hilbert, spaces. The Hohenberg-Kohn mapping between densities and ground states, which is highly complex and nonlocal in coordinate description, is found, for three different model systems, to be simple in metric space, where it becomes a monotonic and nearly linear mapping of vicinities onto vicinities.

Rev. Lett. 106, 050401 (2011)

This talk is part of the Theoretical Physics Seminars series.

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