[Seminar] WIGNER SZFI Szeminárium, jan 30, 14h - Christian Schilling

[Janos Asboth]

*WIGNER SZFI Szeminárium*
Universal upper bounds on the Bose-Einstein condensate

*Christian Schilling*
Clarendon Laboratory, University of Oxford, UK (vendéglátó: Legeza Örs)

2018. január 30, kedd, *14.00*, KFKI Telephely, I. épület 1. emeleti
Tanácsterem
The particle exchange symmetry strongly shapes the behavior of quantum
systems even in the one-particle picture: While fermionic occupation
numbers obey Pauli's exclusion principle, bosons can multiply occupy any
one-particle quantum state and even form a Bose-Einstein condensate. One
may therefore wonder how the situation looks like for hard-core bosons,
fulfilling mixed commutation relations. For N hard-core bosons on an
arbitrary lattice with d sites and independent of additional interaction
terms we prove that the hard-core constraint itself already enforces a
universal upper bound on the Bose-Einstein condensate given by
N_max=(N/d)(d-N+1). This bound can only be attained for one-particle states
with equal amplitudes with respect to the hard-core basis (sites) and when
the corresponding N-particle state  is maximally delocalized. This result
is generalized to the maximum condensate possible within a given
sublattice. We observe that such maximal local condensation is only
possible if the mode entanglement between the sublattice and its complement
is minimal. We also show that the maximizing state is related to the ground
state of a bosonic `Hubbard star' showing Bose-Einstein condensation.

Minden érdeklődőt szívesen látunk!

Asbóth János
szfi-seminar at wigner.mta.hu
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