Laura Foini, Jorge Kurchan
Published 2018-03-28, updated 2018-09-17Version 2
The Eigenstate Thermalization Hypothesis (ETH) implies a form for the matrix elements of local operators between eigenstates of the Hamiltonian, expected to be valid for chaotic systems. Another signal of chaos is a positive Lyapunov exponent, defined on the basis of Loschmidt echo or out-of-time-order correlators. For this exponent to be positive, correlations between matrix elements unrelated by symmetry, usually neglected, have to exist. The same is true for the peak of the dynamic heterogeneity length, relevant for systems with slow dynamics. These correlations, as well as those between elements of different operators, are encompassed in a generalized form of ETH.
The eigenstate thermalization hypothesis beyond standard indicators: emergence of random-matrix behavior at small frequencies
Eigenstate thermalization hypothesis and eigenstate-to-eigenstate fluctuations
Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
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