Apparent low-energy scale invariance in two-dimensional Fermi gases

Recent experiments on a 2D Fermi gas find an undamped breathing mode at twice the trap frequency over a wide range of parameters. To understand this seemingly scale-invariant behavior in a system with a scale, we derive two exact results valid across the entire Bardeen-Cooper-Schrieffer-Bose-Einstein condensation (BCS-BEC) crossover at all temperatures. First, we relate the shift of the mode frequency from its scale-invariant value to γ(d)≡(1+2/d)P-ρ(∂P/∂ρ)(s) in d dimensions. Next, we relate γ(d) to dissipation via a new low-energy bulk viscosity sum rule. We argue that 2D is special, with its logarithmic dependence of the interaction on density, and thus γ(2) is small in both the BCS-BEC regimes, even though P-2ε/d, sensitive to the dimer binding energy that breaks scale invariance, is not.