论文标题
光谱边缘和全息图具有有限截止
Lifshitz tails at spectral edge and holography with a finite cutoff
论文作者
论文摘要
我们提出了Lifshitz尾巴的全息描述，用于$ d = 1 $空间中有界无序系统的一粒子光谱密度。为此，使用了有限截止值的Jackiw-teitelboim（JT）2D Dilaton重力的“聚合物表示”，并且相应的分区函数被视为外部磁场中固定长度的路径上的加权总和。我们确定了小环的状态，负责高斯疾病中LIFSHITZ尾巴的出现，并将混乱的强度与Dilaton的边界价值联系起来。边界理论中对应于泊松症的几何形状涉及在2D平面中坚硬难以穿透的截止盘附近波动的随机路径。结果表明，逃避圆盘的“拉伸”路径的合奏具有波动的kardar-parisi-zhang（kpz）缩放，这是确保Poisson障碍光谱密度的Lifshitz尾巴的双重描述。
We propose the holographic description of the Lifshitz tail typical for one-particle spectral density of bounded disordered system in $D=1$ space. To this aim the "polymer representation" of the Jackiw-Teitelboim (JT) 2D dilaton gravity at a finite cutoff is used and the corresponding partition function is considered as the weighted sum over paths of fixed length in an external magnetic field. We identify the regime of small loops, responsible for emergence of a Lifshitz tail in the Gaussian disorder, and relate the strength of disorder to the boundary value of the dilaton. The geometry corresponding to the Poisson disorder in the boundary theory involves random paths fluctuating in the vicinity of the hard impenetrable cut-off disc in a 2D plane. It is shown that the ensemble of "stretched" paths evading the disc possesses the Kardar-Parisi-Zhang (KPZ) scaling for fluctuations, which is the key property that ensures the dual description of the Lifshitz tail in the spectral density for the Poisson disorder.
