Level statistics of one-dimensional Schrödinger operators with random decaying potential

DOI10.1142/9789814596534_0018zbMath1338.60166arXiv1210.4224OpenAlexW2183698199MaRDI QIDQ2800245

Fumihiko Nakano, Shin'ichi Kotani

Publication date: 15 April 2016

Published in: Festschrift Masatoshi Fukushima (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.4224

zbMATH Keywords

Schrödinger operatorspoint processone-dimensional Schrödinger operatorslevel statisticsrandom decaying potentialrescaled eigenvalues

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Applications of stochastic analysis (to PDEs, etc.) (60H30) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Random operators and equations (aspects of stochastic analysis) (60H25) Diffusion processes and stochastic analysis on manifolds (58J65) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Random linear operators (47B80) Functional limit theorems; invariance principles (60F17) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (9)

Limiting distribution of extremal eigenvalues of d-dimensional random Schrödinger operator ⋮ Poisson Statistics for Anderson Model with Singular Randomness ⋮ Eigenfunction statistics for Anderson model with Hölder continuous single site potential ⋮ Fluctuation of density of states for 1d Schrödinger operators ⋮ Level repulsion for Schrödinger operators with singular continuous spectrum ⋮ Clock statistics for 1d Schrödinger operators ⋮ Shape of eigenvectors for the decaying potential model ⋮ Level statistics for one-dimensional Schrödinger operators and Gaussian beta ensemble ⋮ Spectral fluctuations for Schrödinger operators with a random decaying potential

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