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- W4295693755 abstract "As an extension to the paper by Breuer, Grinshpon, and White cite{B}, we study the linear statistics for the eigenvalues of the Schrodinger operator with random decaying potential with order ${cal O}(x^{-alpha})$ ($alpha>0$) at infinity. We first prove similar statements as in cite{B} for the trace of $f(H)$, where $f$ belongs to a class of analytic functions : there exists a critical exponent $alpha_c$ such that the fluctuation of the trace of $f(H)$ converges in probability for $alpha > alpha_c$, and satisfies a CLT statement for $alpha le alpha_c$, where $alpha_c$ differs depending on $f$. Furthermore we study the asymptotic behavior of its expectation value." @default.
- W4295693755 created "2022-09-14" @default.
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- W4295693755 date "2022-09-10" @default.
- W4295693755 modified "2023-10-18" @default.
- W4295693755 title "Eigenvalue Fluctuations of 1-dimensional random Schrodinger operators" @default.
- W4295693755 doi "https://doi.org/10.48550/arxiv.2209.04608" @default.
- W4295693755 hasPublicationYear "2022" @default.
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