Beecroft Building, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU
Professor Jorge Kurchan, ENS Paris
Benedikt Placke <benedikt.placke@physics.ox.ac.uk>
The “full” Eigenstate Thermalisation Hypothesis and Free Probability.
How does the matrix of a typical operator look in the basis of eigenstates of a chaotic Hamiltonian?
The Eigenstate Thermalization Hypothesis (ETH), developed by Berry, Deutsch, and especially Srednicki in the 1990s, predicts the level of randomness in its matrix elements. However, higher-order correlations between different matrix elements were not considered at the time. A prediction for these correlations became necessary when higher-order expectations emerged as important objects of study.
Introducing a “full” version of ETH, incorporating all possible correlations, led to a proliferation of terms—until the bookkeeping framework of Free Probability came to the rescue, re-establishing simplicity.