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Eigenstate Thermalization Hypothesis and Random Matrix Theory Universality in Few-Body Systems
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Eigenstate Thermalization Hypothesis and Random Matrix Theory Universality in Few-Body Systems
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In this paper, we study the Feingold-Peres model as an example, which is a well-known paradigm of quantum chaos. Using semiclassical analysis and numerical simulations, we study the statistical properties of observables in few-body systems with chaotic classical limits and the emergence of random matrix theory universality. More specifically, we focus on: 1) the applicability of the eigenstate thermalization hypothesis in few-body systems and the dependence of its form on the effective Planck constant and 2) the existence of a universal random matrix theory description of observables when truncated to a small microcanonical energy window. Our results provide new insights into the established field of few-body quantum chaos and help bridge it to modern perspectives, such as the general eigenstate thermalization hypothesis (ETH).
Forward citations
Cited by 3 Pith papers
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Anomalous rate of eigenstate thermalisation at singularities of the density of states
ETH holds with optimal N^{-1} fluctuations for correlated mean-field random matrices in bulk and at regular edges (Haar-like), but N^{-1/2} at cusps, invalidating the Feingold-Peres density-based prediction via multi-...
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Anomalous rate of eigenstate thermalisation at singularities of the density of states
For correlated mean-field random matrices, eigenvector overlaps fluctuate at the Haar scale 1/N in the bulk and at regular edges, and at N^{-1/2} variance near cubic-root cusps, disproving the Feingold–Peres inverse-d...
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Refinements of the Eigenstate Thermalization Hypothesis under Local Rotational Invariance via Free Probability
Under local rotational invariance, the leading factorization of ETH matrix-element correlations is refined by local free cumulants attached to neighboring non-crossing partitions, confirmed numerically in a Floquet sp...
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