ON-LINE QLunch: Giorgio Cipolloni
Speaker: Giorgio Cipolloni
Title: Strong Quantum Unique Ergodicity and its Gaussian fluctuations for Wigner matrices
Abstract: We prove that the eigenvectors of Wigner matrices satisfy the Eignestate Thermalisation Hypothtesis (ETH), which is a strong form of Quantum Unique Ergodicity (QUE) with optimal speed of convergence. Then, using this a priori bound as an input, we analyse the Stochastic Eigenstate Equation (SEE) and prove the Gaussian fluctuations in the QUE.
The main methods behind the above results are: (i) multi-resolvents local laws established via a novel bootstrap scheme; (ii) energy estimates for SEE.
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https://ucph-ku.zoom.us/j/65733505176