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 ${\ensuremath{\gamma}}_{d}\ensuremath{\equiv}(1+2/d)P\ensuremath{-}\ensuremath{\rho}(\ensuremath{\partial}P/\ensuremath{\partial}\ensuremath{\rho}{)}_{s}$ in $d$ dimensions. Next, we relate ${\ensuremath{\gamma}}_{d}$ 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 ${\ensuremath{\gamma}}_{2}$ is small in both the BCS--BEC regimes, even though $P\ensuremath{-}2\ensuremath{\epsilon}/d$, sensitive to the dimer binding energy that breaks scale invariance, is not.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 ${\ensuremath{\gamma}}_{d}\ensuremath{\equiv}(1+2/d)P\ensuremath{-}\ensuremath{\rho}(\ensuremath{\partial}P/\ensuremath{\partial}\ensuremath{\rho}{)}_{s}$ in $d$ dimensions. Next, we relate ${\ensuremath{\gamma}}_{d}$ 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 ${\ensuremath{\gamma}}_{2}$ is small in both the BCS--BEC regimes, even though $P\ensuremath{-}2\ensuremath{\epsilon}/d$, sensitive to the dimer binding energy that breaks scale invariance, is not.

arXiv:1205.1525Physical Review LettersSep 25, 201269 citations

A mean-field study of BCS-BEC crossover

Zhang Deng

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BCS-BEC crossover in two dimensions with Rashba spin-orbit coupling

Lianyi He, Xu-Guang Huang

Sep 26, 20110 citations

d

dimensions. Next, we relate ${\ensuremath{\gamma}}_{d}$ 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 ${\ensuremath{\gamma}}_{2}$ is small in both the BCS--BEC regimes, even though $P\ensuremath{-}2\ensuremath{\epsilon}/d$, sensitive to the dimer binding energy that breaks scale invariance, is not.