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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Okuyama, K. Spectral form factor and semi-circle law in the time direction. J. High Energ. Phys. 2019, 161 (2019). https://doi.org/10.1007/JHEP02(2019)161
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DOI: https://doi.org/10.1007/JHEP02(2019)161