Support theorems for random Schrödinger operators

DOI10.1007/BF01213407zbMath0573.60054MaRDI QIDQ1063326

Shin'ichi Kotani

Publication date: 1985

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

random Schrödinger operatorsinvariant ergodic probability measurelower variation measurerandomness of potentials

Mathematics Subject Classification ID

Random operators and equations (aspects of stochastic analysis) (60H25)

Related Items (17)

Principal Solutions Revisited ⋮ Positive Lyapunov exponents for a class of deterministic potentials ⋮ Localization in general one-dimensional random systems. II: Continuum Schrödinger operators ⋮ Reflectionless Sturm-Liouville equations ⋮ Must the spectrum of a random Schrödinger operator contain an interval? ⋮ On energy gaps in a new type of analytically solvable model in quantum mechanics ⋮ A condition for purely absolutely continuous spectrum for CMV operators using the density of states ⋮ Schrödinger operators with dynamically defined potentials ⋮ Generic spectral results for CMV matrices with dynamically defined Verblunsky coefficients ⋮ Generalized Floquet theory for stationary Schrödinger operators in one dimension ⋮ Lyapunov exponent and rotation number for stochastic Dirac operators ⋮ Unnamed Item ⋮ Remarks on Linear Differential Systems with Measurable Coefficients ⋮ Trace class perturbations and the absence of absolutely continuous spectra ⋮ Spectral theory of random self-adjoint operators ⋮ Zero measure and singular continuous spectra for quantum graphs ⋮ Almost everywhere positivity of the Lyapunov exponent for the doubling map

Cites Work

• Kotani theory for one dimensional stochastic Jacobi matrices
• Sur le spectre des opérateurs aux différences finies aléatoires
• On the spectrum of Schrödinger operators with a random potential
• Unnamed Item
• Unnamed Item

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