Regularity of the rotation number for the one-dimensional time-continuous Schrödinger equation

DOI10.1007/S11040-012-9113-YzbMath1297.35090OpenAlexW2064119214MaRDI QIDQ1928783

Sana Hadj Amor

Publication date: 4 January 2013

Published in: Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11040-012-9113-y

zbMATH Keywords

Schrödinger equationrotation number

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Schrödinger operator, Schrödinger equation (35J10) Perturbations in context of PDEs (35B20) Rotation numbers and vectors (37E45)

Related Items (2)

Absolute continuity of the rotation number for quasi-periodic co-cycles in \(\mathrm{SL}(2,\mathbb R)\) ⋮ Ballistic transport in one-dimensional quasi-periodic continuous Schrödinger equation

Cites Work

• The rotation number for finite difference operators and its properties
• Hölder continuity of the rotation number for quasi-periodic co-cycles in \({SL(2, \mathbb R)}\)
• Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2
• Almost localization and almost reducibility
• Structure of the spectrum of the Schrödinger difference operator with almost-periodic potential in the vicinity of its left edge
• The rotation number for almost periodic potentials
• Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation
• Hölder regularity of integrated density of states for the almost Mathieu operator in a perturbative regime
• Hölder continuity of the integrated density of states for quasi-periodic Schrödinger equations and averages of shifts of subharmonic functions

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