Dynamical bounds for Sturmian Schrödinger operators

DOI10.1016/j.crma.2008.09.019zbMath1156.81021arXiv0906.1932OpenAlexW1963708750MaRDI QIDQ957566

Laurent Marin

Publication date: 28 November 2008

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris, Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.1932

zbMATH Keywords

dynamical boundsquasiperiodical potentialSturmian Schrödinger operators

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Sturm-Liouville theory (34B24) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Statistical mechanics of solids (82D20) Periodic and quasi-periodic flows and diffeomorphisms (37C55) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items

ON- AND OFF-DIAGONAL STURMIAN OPERATORS: DYNAMIC AND SPECTRAL DIMENSION ⋮ Finite section method for aperiodic Schrödinger operators ⋮ Schrödinger operators with dynamically defined potentials ⋮ The Fibonacci Hamiltonian ⋮ Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian ⋮ Transport exponents of Sturmian Hamiltonians

Cites Work

• Unnamed Item
• Unnamed Item
• Power-law bounds on transfer matrices and quantum dynamics in one dimension. II
• Dynamical analysis of Schrödinger operators with growing sparse potentials
• The fractal dimension of the spectrum of the Fibonacci Hamiltonian
• The spectrum of a quasiperiodic Schrödinger operator
• \(\alpha\)-continuity properties of one-dimensional quasicrystals
• Power-law bounds on transfer matrices and quantum dynamics in one dimension
• Hausdorff dimension of spectrum of one-dimensional Schrödinger operator with Sturmian potentials
• Uniform spectral properties of one-dimensional quasicrystals. III: \(\alpha\)-continuity.
• Power law subordinacy and singular spectra. II: Line operators.
• Power-law subordinacy and singular spectra. I: Half-line operators
• Dynamical upper bounds for one-dimensional quasicrystals
• Spectral properties of one dimensional quasi-crystals
• Mixed lower bounds for quantum transport.
• Delocalization in random polymer models
• Transfer matrices and transport for Schrödinger operators.
• Intermittent lower bound on quantum diffusion
• Scaling estimates for solutions and dynamical lower bounds on wavepacket spreading
• Lower transport bounds for one-dimensional continuum Schrödinger operators
• Quantum dynamics and decompositions of singular continuous spectra
• Upper bounds in quantum dynamics
• Dynamical upper bounds on wavepacket spreading

This page was built for publication: Dynamical bounds for Sturmian Schrödinger operators