Conformal-invariance predictions for finite-size and nonhomogeneous systems

Extend conformal-invariance predictions for critical many-body systems to finite-size and non-homogeneous systems, including harmonically trapped Bose gases, beyond the current state of theoretical methods.

Background

The paper establishes scale-invariant universal behavior in finite-size, harmonically trapped Bose gases and suggests that the same experimental platform could test conformal invariance through measurements of higher-order correlations. Such measurements would probe conformal-field-theory predictions in a critical quantum many-body system.

However, the authors explicitly identify the extension of conformal-invariance predictions to finite-size and spatially non-homogeneous systems as an unresolved theoretical challenge. This problem is motivated by the mismatch between standard conformal-field-theory settings and the finite, trapped geometries realized experimentally.

References

At the same time, the extension of conformal-invariance predictions to finite-size and non-homogeneous systems remains an outstanding theoretical challenge, beyond current state-of-the-art methods.

— Universal scaling of fluctuations and correlations across the superfluid transition  (2609.03433 - Paquiez et al., 3 Sep 2026) in Section “Conclusion”