论文标题
在费米和非芬特液体中的拼凑而成
Scrambling versus relaxation in Fermi and non-Fermi liquids
论文作者
论文摘要
我们计算了在广义的sachdev-ye-kitaev模型中表征量子的lyapunov指数，该模型可以通过非弗米液体，通过非弗里米液体来调整来自费米液体的不同温度状态之间的调整，直到快速炒作。由小耦合常数和大$ n $控制的分析计算使我们能够阐明准粒子放松率$ 1/τ$与lyapunov exponent $λ_l$表征scrambling之间的关系。在费米液体状态下，我们发现准粒子弛豫率决定了Lyapunov指数。在$ 1/τ\ gg t $的非fermi液体中，我们发现$λ_l$始终是$ t $ - 与弱耦合限制的耦合常数的预制器。取而代之的是，它取决于表征放松率的缩放指数。 $λ_l$在过渡到快速争夺状态时接近一般上限$2πt$。最后，在边际费米液态状态下，指数在温度下是线性的，预先成品作为非分析函数$ \ sim g \ ln（1/g）$消失，耦合常数$ g $。
We compute the Lyapunov exponent characterizing quantum scrambling in a family of generalized Sachdev-Ye-Kitaev models, which can be tuned between different low temperature states from Fermi liquids, through non-Fermi liquids to fast scramblers. The analytic calculation, controlled by a small coupling constant and large $N$, allows us to clarify the relations between the quasi-particle relaxation rate $1/τ$ and the Lyapunov exponent $λ_L$ characterizing scrambling. In the Fermi liquid states we find that the quasi-particle relaxation rate dictates the Lyapunov exponent. In non-Fermi liquids, where $1/τ\gg T$, we find that $λ_L$ is always $T$-linear with a prefactor that is independent of the coupling constant in the limit of weak coupling. Instead it is determined by a scaling exponent that characterizes the relaxation rate. $λ_L$ approaches the general upper bound $2πT$ at the transition to a fast scrambling state. Finally in a marginal Fermi liquid state the exponent is linear in temperature with a prefactor that vanishes as a non analytic function $\sim g \ln (1/g)$ of the coupling constant $g$.
