Scaling estimates for solutions and dynamical lower bounds on wavepacket spreading

DOI10.1007/BF02807404zbMath1132.81018arXivmath-ph/0407017OpenAlexW2090604431MaRDI QIDQ2470240

David Damanik, Serguei Tcheremchantsev

Publication date: 13 February 2008

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0407017

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Quantum equilibrium statistical mechanics (general) (82B10) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Symbolic dynamics (37B10) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (13)

Ballistic transport for the Schrödinger operator with limit-periodic or quasi-periodic potential in dimension two ⋮ Zero-measure Cantor spectrum for Schrödinger operators with low-complexity potentials ⋮ Quantum Hamiltonians with quasi-ballistic dynamics and point spectrum ⋮ Schrödinger operators with dynamically defined potentials ⋮ Dynamical bounds for Sturmian Schrödinger operators ⋮ Quantum dynamics via complex analysis methods: general upper bounds without time-averaging and tight lower bounds for the strongly coupled Fibonacci Hamiltonian ⋮ Eigenvalue spacings and dynamical upper bounds for discrete one-dimensional Schrödinger operators ⋮ Lower transport bounds for one-dimensional continuum Schrödinger operators ⋮ The Fibonacci Hamiltonian ⋮ Ballistic transport for Schrödinger operators with quasi-periodic potentials ⋮ Almost ballistic transport for the weakly coupled Fibonacci Hamiltonian ⋮ Upper bounds in quantum dynamics ⋮ Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian

Cites Work

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• Half-line Schrödinger operators with no bound states
• Power-law bounds on transfer matrices and quantum dynamics in one dimension. II
• Dynamical analysis of Schrödinger operators with growing sparse potentials
• The spectrum of a quasiperiodic Schrödinger operator
• On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators
• The absolute continuous spectrum of one-dimensional Schrödinger operators with decaying potentials
• \(\alpha\)-continuity properties of one-dimensional quasicrystals
• Power-law bounds on transfer matrices and quantum dynamics in one dimension
• Sparse potentials with fractional Hausdorff dimension.
• Uniform spectral properties of one-dimensional quasicrystals. III: \(\alpha\)-continuity.
• Power law subordinacy and singular spectra. II: Line operators.
• Uniform spectral properties of one-dimensional quasicrystals. I: Absence of eigenvalues
• Power-law subordinacy and singular spectra. I: Half-line operators
• Spectral properties of one dimensional quasi-crystals
• Stability of singular spectral types under decaying perturbations
• Mixed lower bounds for quantum transport.
• Delocalization in random polymer models
• Transfer matrices and transport for Schrödinger operators.
• Schrödinger semigroups
• Dynamical upper bounds on wavepacket spreading
• Log-dimensional spectral properties of one-dimensional quasicrystals
• Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators

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