Apparent low-energy scale invariance in two-dimensional Fermi gases.
Apparent low-energy scale invariance in two-dimensional Fermi gases.
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DOI：
10.1103/physrevlett.109.135301
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发表时间：
2012-05
影响因子：
8.6
通讯作者：
E. Taylor;M. Randeria
中科院分区：
文献类型：
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作者：
E. Taylor;M. Randeria
最近对二维费米气体的实验发现了在宽参数范围内两倍陷阱频率的无阻尼呼吸模式。为了理解具有尺度的系统中这种看似尺度不变的行为，我们得出了在所有温度下的整个 Bardeen-Cooper-Schrieffer-Bose-Einstein 凝聚 (BCS-BEC) 交叉中有效的两个精确结果。首先，我们将模态频率从其尺度不变值的偏移与 d 维中的 γ(d)eq(1+2/d)P-ρ(∂P/∂ρ)(s) 联系起来。接下来，我们通过新的低能体积粘度和规则将 γ(d) 与耗散联系起来。我们认为 2D 是特殊的，其相互作用对密度呈对数依赖性，因此 γ(2) 在两种 BCS-BEC 体系中都很小，尽管 P-2ε/d 对破坏尺度不变性的二聚体结合能敏感，但不是很小。
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.