Spectral form factor for time-dependent matrix model

Abstract

Abstract The quantum chaos is related to a Gaussian random matrix model, which shows a dip-ramp-plateau behavior in the spectral form factor for the large size N. The spectral form factor of time dependent Gaussian random matrix model shows also dip-ramp-plateau behavior with a rounding behavior instead of a kink near Heisenberg time. This model is converted to two matrix model, made of M 1 and M 2. The numerical evaluation for finite N and analytic expression in the large N are compared for the spectral form factor.

Keywords

• 1/N Expansion
• Matrix Models
• Random Systems