Eigenstate Thermalization Hypothesis for Wigner-type Matrices
Volodymyr Riabov, L\'aszl\'o Erd\H{o}s
TL;DR
This paper proves the Eigenstate Thermalization Hypothesis for Wigner-type matrices, demonstrating that quantum states in these matrices exhibit thermalization behavior with precise fluctuation control.
Contribution
It establishes the ETH for Wigner-type matrices in the bulk spectrum with optimal fluctuation bounds and introduces rank-uniform local laws for resolvents.
Findings
ETH holds for Wigner-type matrices in the bulk spectrum.
Optimal fluctuation control for arbitrary rank observables.
Development of rank-uniform local laws for resolvents.
Abstract
We prove the Eigenstate Thermalization Hypothesis for general Wigner-type matrices in the bulk of the self-consistent spectrum, with optimal control on the fluctuations for observables of arbitrary rank. As the main technical ingredient, we prove rank-uniform optimal local laws for one and two resolvents of a Wigner-type matrix with regular observables.
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Taxonomy
TopicsMatrix Theory and Algorithms · Spectral Theory in Mathematical Physics · Statistical Mechanics and Entropy