1112.1384 (Johannes Hofmann)

Quantum anomaly, universal relations, and breathing mode of a
two-dimensional Fermi gas    [PDF]

Johannes Hofmann

In this paper, we show that the hidden SL(2,R) symmetry of a harmonically
trapped Fermi gas in two dimensions is broken by quantum effects. The anomalous
correction to the symmetry algebra is given by a two-body operator which is
well-known as the contact. Taking into account this modification, we are able
to derive the virial theorem for the system and a universal relation for the
pressure of a homogeneous gas. The existence of an undamped breathing mode is
associated with the classical symmetry. We provide an estimate for the
anomalous frequency shift of this oscillation at zero temperature and compare
the result with a recent experiment by [E. Vogt et al., Phys. Rev. Lett. 108,
070404 (2012)]. Discrepancies are attributed to finite temperature effects.

View original: http://arxiv.org/abs/1112.1384