Entanglement Induced Fluctuations of Cold Bosons

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We show that due to entanglement, quantum fluctuations may differ significantly from statistical fluctuations. We calculate quantum fluctuations of the particle number and of the energy in a sub-volume of a system of bosons in a pure state, and briefly discuss the possibility of measuring them. We find that energy fluctuations have a non-extensive nature.
Replaced with published version. Added calculations, explanations and clarifications, results unchanged

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