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- W4367694570 abstract "We investigate analytically and numerically the eigenstate thermalization hypothesis (ETH) in terms of a Hermitian operator in the eigenkets selected from the elements of a real (complex) symmetric random matrix of the Gaussian orthogonal ensemble (Gaussian unitary ensemble) according to the theory of random matrices. We propose a method to construting the commensurate eigenvector basis that are appropriate for the numerical calculation as well as the diagonal or off-diagonal ETH diagnostics. We also investigate the integrablity-chaos transition with independent perturbations in terms of the Berry autocorrelation in semicalssical limit, where there is a phase space spanned by the momentum-like projection and the range of local wave function. In such a semiclassical framework, we further develop a method which is base on the correlations of adjacent local points (CALP), to investigate the integrablity-chaos transition In the presence of uncorrelated peturbations and correlated integrable eigenstate fluctuations, which is applicable for both the ergodic and nonergodic systems (where the Berry autocorrelation is vanishingly small and be nearly one, respectively, similar to the characteristic of inverse participation ratio (IPR)).More importantly,this work reveals and illustrates to a certain extent the essential role of the Golden ratio and the constant 31 in the quantum chaos physics." @default.
- W4367694570 created "2023-05-03" @default.
- W4367694570 creator A5029061017 @default.
- W4367694570 date "2023-05-01" @default.
- W4367694570 modified "2023-09-28" @default.
- W4367694570 title "Eigenstate thermalization and integrability-chaos transition base on the commensurate eigenvector basis and the correlations of adjacent local points" @default.
- W4367694570 doi "https://doi.org/10.48550/arxiv.2305.00662" @default.
- W4367694570 hasPublicationYear "2023" @default.
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