In many papers in Random Matrix Theory [1-3] related to quantum chaos (and, in particular, to the SYK model) they analytically continuate the partition function of the system $Z(\beta)$ into $Z(\beta + it)$ and then define the Spectral Form Factor like

\begin{equation} g(\beta,t)=\langle Z^*Z\rangle \end{equation}

They then claim that the specific shape of this function gives a lot of information about the level statistics of the system. Is there any paper or book where I can read a good introduction on these tools? Every paper I found doesn't explain anything in great detail and just shows graphs.

[1] https://arxiv.org/abs/1806.05316

[2] https://arxiv.org/abs/1706.07439

[3] https://arxiv.org/abs/1611.04650


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