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Eigenstate thermalization, quantum designs and free probability

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If you have a question about this talk, please contact Bo Peng.

The Eigenstate Thermalization Hypothesis needs to be completed to take into account higher correlators, for example to compute out of time order operators (OTOCs). Once this is done, a Pandora’s box of contributions is opened. As it turns out, the instrument for organizing this has been around for a few decades: it is the technique of Free Probability. Once Free Probability is taken on board, one finds an immediate connection with Unitary Designs, a construction of a set of unitary matrices that can be taken as a proxy for the whole unitary group, a subject that has attracted considerable interest in quantum information.

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