Spectral form factor and semi-circle law in the time direction
Kazumi Okuyama · Journal of High Energy Physics · 2019
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.