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arXiv · 1811.09988

Spectral form factor and semi-circle law in the time direction

Kazumi Okuyama
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Abstract

We study the time derivative of the connected part of spectral form factor, which we call the slope of ramp, in Gaussian matrix model. We find a closed formula of the slope of ramp at finite $N$ with non-zero inverse temperature. Using this exact result, we confirm numerically that the slope of ramp exhibits a semi-circle law as a function of time.

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Kazumi Okuyama. 2019-02-13. Spectral form factor and semi-circle law in the time direction. https://doi.org/10.1007/jhep02(2019)161

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