Level statistics for one-dimensional Schrödinger operators and Gaussian beta ensemble

DOI10.1007/s10955-014-0987-xzbMath1303.82019arXiv1312.6901OpenAlexW3099505683MaRDI QIDQ458421

Fumihiko Nakano

Publication date: 7 October 2014

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.6901

zbMATH Keywords

random Schrödinger operatorslevel statisticsbeta ensemble

Mathematics Subject Classification ID

Random operators and equations (aspects of stochastic analysis) (60H25) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Random matrices (algebraic aspects) (15B52)

Related Items (16)

Coulomb and Riesz gases: The known and the unknown ⋮ Logarithmic, Coulomb and Riesz energy of point processes ⋮ Limiting distribution of extremal eigenvalues of d-dimensional random Schrödinger operator ⋮ The \(\mathrm{Sine}_{\beta}\) operator ⋮ Fluctuation of density of states for 1d Schrödinger operators ⋮ Uniform point variance bounds in classical beta ensembles ⋮ Large deviation principle for empirical fields of log and Riesz gases ⋮ Level repulsion for Schrödinger operators with singular continuous spectrum ⋮ Localization crossover for the continuous Anderson Hamiltonian in 1-d ⋮ Clock statistics for 1d Schrödinger operators ⋮ Shape of eigenvectors for the decaying potential model ⋮ The maximum deviation of the \(\mathrm{sine}_\beta\) counting process ⋮ Eigenvectors of the 1-dimensional critical random Schrödinger operator ⋮ Spectral fluctuations for Schrödinger operators with a random decaying potential ⋮ Spectral statistics for one-dimensional Anderson model with unbounded but decaying potential ⋮ Operator limit of the circular beta ensemble

Cites Work

• The scaling limit of the critical one-dimensional random Schrödinger operator
• Continuum limits of random matrices and the Brownian carousel
• Eigenvalue statistics for CMV matrices: From Poisson to clock via random matrix ensembles
• One-dimensional Schrödinger operators with random decaying potentials
• Level statistics of one-dimensional Schrödinger operators with random decaying potential

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