| Numéro |
J. Phys. France
Volume 50, Numéro 7, avril 1989
|
|
|---|---|---|
| Page(s) | 707 - 716 | |
| DOI | https://doi.org/10.1051/jphys:01989005007070700 | |
J. Phys. France 50, 707-716 (1989)
DOI: 10.1051/jphys:01989005007070700
L.D. Landau Institute for Theoretical Physics, Moscow, U.S.S.R.
0365G - Solutions of wave equations: bound states.
0365F - Algebraic methods.
0210 - Logic, set theory, and algebra.
Key words
fractals -- quantum theory -- renormalisation -- Schrodinger equation -- set theory
DOI: 10.1051/jphys:01989005007070700
Renormalization group for a quasiperiodic Schrödinger operator
L.S. LevitovL.D. Landau Institute for Theoretical Physics, Moscow, U.S.S.R.
Abstract
The real-space renormalization group for a generalized Fibonacci Hamiltonian is constructed. The spectrum is shown to have the hierarchical structure of a zero-measure Cantor set guided by the continuous fraction representation of the incommensurate frequency ω of the problem. The fractal properties of the spectrum are discussed.
Résumé
Nous construisons un groupe de renormalisation dans l'espace réel pour hamiltonien de Fibonacci généralisé. Nous montrons que le spectre a la structure hiérarchique d'un ensemble de Cantor de mesure nulle lié à la représentation en fraction continue de la fréquence incommensurable du problème. Nous discutons des propriétés fractales du spectre.
0365G - Solutions of wave equations: bound states.
0365F - Algebraic methods.
0210 - Logic, set theory, and algebra.
Key words
fractals -- quantum theory -- renormalisation -- Schrodinger equation -- set theory