Dresden 2017 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 29: Other Low Temperature Topics: Cold Atomic Gases
TT 29.1: Vortrag
Dienstag, 21. März 2017, 12:00–12:15, HSZ 201
Universal upper bound on the condensate-concentration of lattice hard-core bosons — Felix Tennie1, Vlatko Vedral1,2, and •Christian Schilling1 — 1Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom — 2Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
To investigate Bose-Einstein condensation for interacting bosons, usually the largest eigenvalue of their one-particle reduced density matrix is calculated. For lattice systems of N hard-core bosons on d sites we take a complementary viewpoint: Independent of the spatial dimension and any further microscopic details we prove that the hard-core constraint enforces a universal upper bound on occupation numbers given by Nmax=(N/d)(d−N+1). It can only be attained for one-particle states |ϕ⟩ with equal amplitudes with respect to the hard-core basis (sites) and when the corresponding N-particle state |Ψ⟩ is maximally delocalized. We show that the maximizing state |Ψ⟩ is related to the ground state of a bosonic ‘Hubbard star’ showing Bose-Einstein condensation.