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The Rate of Convergence in the Quantum Central Limit Theorem and Applications

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I will discuss a Berry—Esseen bound for local observables on quantum lattice systems. It bounds the rate at which macroscopic fluctuations approach normality. Presented applications include the normality of the density of states, the local equivalence of microcanonical and canonical ensembles, and, in the setting of quantum quenches, the local thermalization under random Hamiltonians and a bound on the effective dimension (or inverse participation ratio or purity) of equilibrium states.

This talk is part of the CQIF Seminar series.

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