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Title:
Eigenstate Thermalization and Locality
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Abstract:
Eigenstate Thermalization Hypothesis (ETH) is a set of properties which explain the emergence of equilibrium statistical mechanics for an isolated quantum chaotic system. It is believed to be a characteristic feature, and even used as a working definition, of quantum chaos. At the technical level ETH can be understood as an ansatz for the matrix elements of certain observables. We start by showing how ETH can help define a novel order parameter which would distinguish chaotic and non-chaotic phases. We then proceed by constraining the ETH ansatz in case of the systems with local interactions. For the systems exhibiting diffusive transport we find a new stringent bound limiting applicability of Random Matrix Theory to describe the observables satisfying the ETH.
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