Coherent Bose-Einstein condensation with fluctuating density

arXiv:2607.12926 2026 Architecture 1 ideas extracted · analyzed Aug 30, 2026

What the math gives to ML

The paper separates coherent phase from strongly fluctuating condensate density. For an ideal grand-canonical condensate, the occupation-number distribution determines the full correlation hierarchy, and the large-density coherent-power ratio approaches pi divided by 4 rather than one. A transferable neural analogue is a complex hidden or latent variable with a persistent phase and an explicitly sampled amplitude, combined with a moment regularizer that tests whether amplitude fluctuations follow the predicted hierarchy.

Ideas from this paper

Unverified 2026

Coherent-Fluctuating Amplitude Units

Represent selected hidden features as z = sqrt(N) exp(i theta), with a persistent phase and an explicitly stochastic amplitude. Regularize the ratio between coherent power |E[z]|^2 and total power E[|z|^2] toward the condensate prediction pi/4, while optionally matching higher amplitude moments.

Useful4/10
Difficulty5/10
Novelty8/10
Paper: Coherent Bose-Einstein condensation with fluctuating density arXiv:2607.12926