Apparent low-energy scale invariance in two-dimensional Fermi gases
arXiv:1205.1525 · doi:10.1103/PhysRevLett.109.135301
Abstract
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 BCS-BEC crossover at all temperatures. First, we relate the shift of the mode frequency from its scale-invariant value to in dimensions. Next, we relate 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 is small in both the BCS and BEC regimes, even though , sensitive to the dimer binding energy that breaks scale invariance, is not.
Published version. 7 pages, 4 figures. Includes supplemental material
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