Coherent Bose-Einstein condensation with fluctuating density
Abstract
Bose-Einstein condensation in the grand canonical ensemble admits a formulation in terms of a phase-density decomposition of the condensate mode operator ψ̂bf 0. In the presence of macroscopic condensate number fluctuations this representation presents nontrivial implications. In particular, we show that, for the ideal gas, under the assumption of a well-defined phase and a fluctuating condensate density, the square modulus of the anomalous average ⟨ ψ̂bf 0⟩ can provide only a fraction of the whole condensate density ρbf 0 and for the grand canonical statistics of the ideal Bose gas one obtains the value |⟨ ψ̂bf 0⟩|2 =(π/4) ρbf 0. The remaining part is supplemented by the (macroscopic) fluctuations of ψ̂bf 0, which become a distinctive feature of the BEC in this setting. This provides a transparent physical picture of a condensate of photons with a well-defined phase but large number fluctuations, as observed in dye-filled microcavity photon experiments. We also propose a way to access the square modulus of the anomalous average to test theoretical predictions.
Versions
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BibTeX
@misc{salasnich2026coherent,
title = {{Coherent Bose-Einstein condensation with fluctuating density}},
author = {L. Salasnich and A. Crisanti and A. Sarracino and M. Zannetti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.12926},
eprint = {2607.12926},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.12926},
}
RIS
TY - UNPB
TI - Coherent Bose-Einstein condensation with fluctuating density
AU - L. Salasnich
AU - A. Crisanti
AU - A. Sarracino
AU - M. Zannetti
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2607.12926
UR - https://arxiv.org/abs/2607.12926
AB - Bose-Einstein condensation in the grand canonical ensemble admits a formulation in terms of a phase-density decomposition of the condensate mode operator ψ̂_bf 0. In the presence of macroscopic condensate number fluctuations this representation presents nontrivial implications. In particular, we show that, for the ideal gas, under the assumption of a well-defined phase and a fluctuating condensate density, the square modulus of the anomalous average ⟨ ψ̂_bf 0⟩ can provide only a fraction of the whole condensate density ρ_bf 0 and for the grand canonical statistics of the ideal Bose gas one obtains the value |⟨ ψ̂_bf 0⟩|^2 =(π/4) ρ_bf 0. The remaining part is supplemented by the (macroscopic) fluctuations of ψ̂_bf 0, which become a distinctive feature of the BEC in this setting. This provides a transparent physical picture of a condensate of photons with a well-defined phase but large number fluctuations, as observed in dye-filled microcavity photon experiments. We also propose a way to access the square modulus of the anomalous average to test theoretical predictions.
ER -