论文标题
双尺度SYK模型中的光谱形态
Spectral form factor in the double-scaled SYK model
论文作者
论文摘要
在本说明中，我们在无限温度下以大$ q $限制的SYK模型中的光谱形式。我们为描述频谱形式因子时间依赖性的斜率和坡道区域的鞍点方程构建了分析解。这些鞍点是通过采用不同的$ Q $限制的不同方法来获得的：斜率区域由复制式 - 二角溶液描述，而坡道区域则通过复制 - 非对角线溶液描述。我们发现，坡道行为的开始发生在订单$ q \ log q $的无用时间。我们还评估了深层坡度和坡道溶液的一环校正，并研究了从坡度到坡道的过渡。我们表明，这种过渡伴随着扰动$ 1/q $扩展的故障，并且无用的时间是通过将这种扩展到后期推断到后期的一致性来定义的。
In this note we study the spectral form factor in the SYK model in large $q$ limit at infinite temperature. We construct analytic solutions for the saddle point equations that describe the slope and the ramp regions of the spectral form factor time dependence. These saddle points are obtained by taking different approaches to the large $q$ limit: the slope region is described by a replica-diagonal solution and the ramp region is described by a replica-nondiagonal solution. We find that the onset of the ramp behavior happens at the Thouless time of order $q \log q$. We also evaluate the one-loop corrections to the slope and ramp solutions for late times, and study the transition from the slope to the ramp. We show this transition is accompanied by the breakdown of the perturbative $1/q$ expansion, and that the Thouless time is defined by the consistency of extrapolation of this expansion to late times.
