Discrete magnetic Laplacian
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Publication:1335243
DOI10.1007/BF02101702zbMath0811.46079MaRDI QIDQ1335243
Publication date: 27 September 1994
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
integrated density of statesmagnetic Schrödinger operatoralmost Mathieu operatordiscrete magnetic Laplacian\(\text{II}_ 1\)-factorAMDMLIDS
Applications of operator theory in the physical sciences (47N50) Applications of selfadjoint operator algebras to physics (46L60) Applications of functional analysis in quantum physics (46N50)
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Cites Work
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- Scaling for the discrete Mathieu equation
- Purely absolutely continuous spectrum for almost Mathieu operators
- Localization for a class of one dimensional quasi-periodic Schrödinger operators
- On the measure of the spectrum for the almost Mathieu operator
- Log Hölder continuity of the integrated density of states for stochastic Jacobi matrices
- A metal-insulator transition for the almost Mathieu model
- Almost periodic Schrödinger operators. II: The integrated density of states
- Almost periodic Schrödinger operators: A review
- Remark on the continuity of the density of states of ergodic finite difference operators
- Cantor spectrum for the almost Mathieu equation
- Two-dimensional Schrödinger operators in periodic fields
- Gauss polynomials and the rotation algebra
- The coexistence problem for the discrete Mathieu operator
- The rotation number for almost periodic potentials
- C*-algebras associated with irrational rotations
- On spectral properties of almost Mathieu operators and connections with irrational rotation \(C^*\)-algebras
- 1\(D\)-quasiperiodic operators. Latent symmetries
- A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants
- Anderson localization for the almost Mathieu equation: A nonperturbative proof
- Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential
- Absence of Cantor spectrum for a class of Schrödinger operators
- Analyse semi-classique pour l'équation de Harper (avec application à l'équation de Schrödinger avec champ magnétique)
- The positivity of the Lyapunov exponent and the absence of the absolutely continuous spectrum for the almost-Mathieu equation
- Almost Mathieu Operators and Rotation C* -Algebras
- Absence of localisation in the almost Mathieu equation
- THE SPECTRAL THEORY AND THE INDEX OF ELLIPTIC OPERATORS WITH ALMOST PERIODIC COEFFICIENTS
- A sum rule for the dispersion relations of the rational Harper equation
- Simplicity of C* -Algebras of Minimal Dynamical Systems
- THE STATE DENSITY AND OTHER SPECTRAL INVARIANTS OF SELFADJOINT ELLIPTIC OPERATORS WITH RANDOM COEFFICIENTS
- SPECTRA OF RANDOM SELF ADJOINT OPERATORS
- Semi-classical analysis for Harper's equation. III : Cantor structure of the spectrum
- Single Band Motion of Conduction Electrons in a Uniform Magnetic Field