At large scales, many diverse processes obey the law of large numbers. Whenever many weakly correlated variables contribute to the same quantity, the latter are expected to have Gaussian typical fluctuations.

However, there are exceptions to this common scenario!

In this preprint, we investigate the typical fluctuations of the integrated spin-current in the XXZ quantum spin chain in the so-called easy axis regime. Using ballistic macroscopic fluctuation theory, we analytically show the emergence of a "nested-Gaussian" distribution, previously only numerically observed.

Takato Yoshimura, Žiga Krajnik, Alvise Bastianello, Enej Ilievski, arXiv:2602.24242 (2026)

Besides the already interesting axial-regime, we hope this approach will help further understanding the even more intriguing isotropic regime, which has an intimate, but not fully disclosed, connection with the KPZ universality class.

The Pauli exclusion principle is a cornerstone of quantum physics: in the ground state, fermions occupy the lowest-energy levels forming a Fermi sea. In one-dimension, when interactions are deeply linked to statistics, even interacting bosons feature emergent Fermi seas universally described by the Tomonaga-Luttinger liquid approach. In these partner preprints, we show that generalizations of Fermi seas with a fractional occupancy can be realized in ultracold bosons out of equilibrium!

In this theoretical preprint, we show how fractional Fermi seas can be realized through cyclic changes in the interactions in the 1d Bose gas. Correlation functions in these states feature a new form of criticality, beyond the Tomonaga-Luttinger liquid

Exotic critical states as fractional Fermi seas in the one-dimensional Bose gas, A. Bastianello, Y. Zeng, S. Dhar, Z. Wang, X. Yu, M. Horvath, G. E. Astrakharchik, Y. Guo, H.-C. Nägerl, M. Landini, arXiv:2602.17656 (2026)

As a cherry on top, fractional Fermi seas are realized in practice in ultracold Cesium atoms, and they imprint Friedel oscillations in the one-body correlation function

Realization of fractional Fermi seas, Y. Zeng, A. Bastianello, S. Dhar, Z. Wang, X. Yu, M. Horvath, G. E. Astrakharchik, Y. Guo, H.-C. Nägerl, M. Landini, arXiv:2602.17657 (2026)

Correlation functions lie at the core of our understanding of many-body phenomena, and in particular unequal-time correlations detect the emergence of hydrodynamics. In contrast with general systems following the Fick law, which behave diffusively, integrable models show ballistic behavior in correlation functions.

In a new preprint, we observe ballistic correlation functions in a photonic platform whose dynamics is well-described by the Nonlinear Schroedinger equation, and compare observations with predictions from GHD.

E. Charnay, A. Escoubet, F. Copie, S. Randoux, T. Bonnemain, A. Bastianello, P. Suret, arXiv:2601.21085 (2026)

A special thanks goes to Elias Charnay who collected such great experimental data!