Quantum Anomalies
We are interested in the rare examples of systems with no length scales and in the consequences of weak breaking of this property. One of the most prominent properties of scale-free gases is the monochromaticity of the breathing excitations: their frequency is strictly fixed to be the double of the trapping frequency, for any amplitude. In the case of two-dimensional Bose gases, the departure from this law may occur due to quantum effects (the so-called quantum anomaly) [OPL10], and due to the weak residual interaction with the third dimension[MDL13] (see the results of our experimental-theoretical study on the left).
Similar results are obtained for one-dimensional p-wave-interacting fermions, and for bosons near the Tonks-Girardeau regime[CDZO15],[ZAA14].
The quantum anomaly predicted in [OPL10] has been observed experimentally [Murthy et al, arXiv:1805.04734; Peppler et al, arXiv:1804.05102].
Triangular breathers
In [ODTGDA21], we reinterpreted the triagular BEC breathers, observed in [Saint-Jalm et al, Phys. Rev. X 9, 021035 (2019)] and explained on [Shi et al, arXiv:2011.01415 (2020)], in terms of Damski-Chandrasekhar's shock waves.
In [TDGAO22], we explain the period-T/7 quasi-breathing observed for the disk breathers in [Saint-Jalm et al, Phys. Rev. X 9, 021035 (2019)], as a curious coincidence.