论文标题
单粒子量子混乱的多体水平统计
Many-body level statistics of single-particle quantum chaos
论文作者
论文摘要
我们考虑一个单一随机矩阵集合的非相互作用的多屈光度系统（等效于Q = 2复杂的Sachdev-ye-Kitaev模型） - 单粒子量子混乱的通用模型。我们通过使用随机矩阵理论的代数方法来分析频谱形态来研究相应的许多粒子水平统计，并与精确的数值模拟匹配。尽管该理论具有整合性，但发现多体频谱刚度具有令人惊讶的丰富景观。特别是，我们发现由单粒子混乱引起的遥远多体水平的残余排斥以及水平吸引的岛屿。这些结果被编码在光谱形式因子中的指数坡道中，我们表明这是嵌入混乱介质中的非共性多个弗米尔系统的通用特征。
We consider a non-interacting many-fermion system populating levels of a unitary random matrix ensemble (equivalent to the q=2 complex Sachdev-Ye-Kitaev model) - a generic model of single-particle quantum chaos. We study the corresponding many-particle level statistics by calculating the spectral form factor analytically using algebraic methods of random matrix theory, and match it with an exact numerical simulation. Despite the integrability of the theory, the many-body spectral rigidity is found to have a surprisingly rich landscape. In particular, we find a residual repulsion of distant many-body levels stemming from single-particle chaos, together with islands of level attraction. These results are encoded in an exponential ramp in the spectral form-factor, which we show to be a universal feature of non-ergodic many-fermion systems embedded in a chaotic medium.
