Year: 2017
Type: article
Abstract: 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 nonexponential 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 for systems with a discrete energy spectrum. We find the spectral form factor in a number of illustrative models; notably, we obtain the exact answer in the Gaussian unitary ensemble for any $N$ with excellent agreement with recent numerical studies. We also discuss the relationship of our findings to models of black hole information loss, such as the Sachdev-Ye-Kitaev model dual to ${\mathrm{AdS}}_{2}$, as well as higher-dimensional versions of AdS/CFT.
Authors: A. del Campo, J. Molina-Vilaplana, J. Sonner
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G2093796315, G529604792, G7957937980
OpenAlex ID: W2588723549