论文标题
sachdev-ye-kitaev模型：能量谱的非自动平均特性
Sachdev-Ye-Kitaev model: Non-self-averaging properties of the energy spectrum
论文作者
论文摘要
Sachdev-Ye-Kitaev模型（SYK）的短时间（大能量）行为是该模型增强兴趣增长的主要动机之一。真正的混沌行为在无用的时间内设置为可以从能量谱中提取。为了这样做，有必要展开频谱，即滤除全球趋势。使用简单的合奏平均值进行展开，从而导致对无能的能量的参数估计。通过检查频谱的行为，随着矩阵元素的分布而变为对数正态分布，表明样品级别间距方差确定了对无能的能量的估计。使用奇异值分解方法SVD，将这些样品滤除到样品波动中，无用的能量在参数上变大了，本质上是带宽的顺序。结果表明，即使在热力学极限中，SYK模型即使在考虑其短时间特性时也必须考虑到它。
The short time (large energy) behavior of the Sachdev-Ye-Kitaev model (SYK) is one of the main motivation to the growing interest garnered by this model. True chaotic behaviour sets in at the Thouless time, which can be extracted from the energy spectrum. In order to do so, it is necessary to unfold the spectrum, i.e., to filter out global tendencies. Using a simple ensemble average for unfolding results in a parametically low estimation of the Thouless energy. By examining the behavior of the spectrum as the distribution of the matrix elements is changed into a log-normal distribution it is shown that the sample to sample level spacing variance determines this estimation of the Thouless energy. Using the singular value decomposition method, SVD, which filters out these sample to sample fluctuations, the Thouless energy becomes parametrically much larger, essentially of order of the band width. It is shown that the SYK model in non-self-averaging even in the thermodynamic limit which must be taken into account in considering its short time properties.
