Dresden 2020 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 67: Cold Atomic Gases and Superfluids

TT 67.4: Vortrag

Donnerstag, 19. März 2020, 17:15–17:30, HSZ 204

Reduced-density-matrix functional theory for the N-boson Hubbard model: Universal functionals, v-representability and quantum depletion as emerging phenomenon — •Jakob Wolff1, Carlos Benavides-Riveros1, Christian Schilling2,3, and Miguel Alexandre Lopes Marques11Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06120 Halle (Saale), Germany — 2Department of Physics, Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, 80333 München, Germany — 3Wolfson College, University of Oxford, Oxford OX2 6UD, United Kingdom

The Hohenberg-Kohn theorem and its generalization to non-local external potentials initiated the development of density and one-matrix functional theory. While such methods were applied so far only to fermionic quantum systems, the realization of ultracold gases urges the development of analogous bosonic functionals. In the form of the Hubbard dimer model for arbitrary number of bosons, we study the building block of one-dimensional optical lattices. Close to the Bose-Einstein condensation (BEC), we determine the one-matrix functional analytically. Remarkably, its gradient is found and proven to diverge repulsively in the regime of almost complete BEC. This possibly provides in particular a more fundamental explanation than the concept of quantum depletion for the absence of BEC of full degree in nature. Moreover, we obtain an analytic description of the set of v-representable one-body matrices for all N.

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