1205.1525 (Edward Taylor et al.)

Apparent low-energy scale invariance in two-dimensional Fermi gases    [PDF]

Edward Taylor, Mohit Randeria

Motivated by recent experiments on the monopole breathing mode of a 2d Fermi gas which suggest scale-invariant behavior independent of interactions, we derive two exact results valid across the entire BCS-BEC crossover and at all temperatures. We relate the shift of the mode frequency from twice the trap frequency to $\gamma_d \equiv (1+2/d)P-\rho(\partial P/\partial\rho)_s$ in $d$ dimensions. We next show that $\gamma_d$, a measure of the deviation from scale invariance, is equal to a low-energy sum rule of the bulk viscosity spectral function. We argue that 2d, with its logarithmic dependence of the coupling constant on density, is special and that $\gamma_2$ is small in both the BCS and BEC regimes, despite the fact that $P-2\varepsilon/d$, sensitive to the dimer binding energy scale that breaks scale invariance, is not.

View original: http://arxiv.org/abs/1205.1525