Scrambling the spectral form factor: unitarity constraints and exact results

Understand

Quantum speed limits set an upper bound to the rate at which a quantum system can evolve and as such can be used to analyze the scrambling of information.

• To this end, we consider the survival probability of a thermofield double state under unitary time-evolution which is related to the analytic continuation of the partition function.
• We provide an exponential lower bound to the survival probability with a rate governed by the inverse of the energy fluctuations of the initial state.
• Further, we elucidate universal features of the non-exponential behavior at short and long times of evolution that follow from the analytic properties of the survival probability and its Fourier transform, both for systems with a continuous and a discrete energy spectrum.