The universality of chaotic many-body dynamics has long been identified by random matrix theory, leading to the Eigenstate Thermalization Hypothesis (ETH).
In this lecture, I will present the full version of ETH, which encompasses correlations among matrix elements needed to describe dynamical correlations of different times. Then, I will show how this ansatz can be highly simplified by the use of Free Probability theory, an extension of probability for non-commuting random variables.
References:
- L. Foini and J. Kurchan, Eigenstate thermalization hypothesis and out of time order correlators, Phys. Rev. E 99, 042139 (2019); - S. Pappalardi, L. Foini and J. Kurchan, Eigenstate thermalization hypothesis and free probability, Phys. Rev. Lett. 129, 170603 (2022); - Lecture notes "Free Probability Approaches to (chaotic) Quantum Dynamics" by S. Pappalardi