Minimal configurations for the Frenkel-Kontorova model on a quasicrystal

DOI10.1007/s00220-006-1531-xzbMath1104.82014arXivmath-ph/0511012OpenAlexW2013697769MaRDI QIDQ863125

Pierre Guiraud, Jean-Marc Gambaudo, Samuel Petite

Publication date: 25 January 2007

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0511012

zbMATH Keywords

rotation numberAubry-Mather theoryquasicrystalFrenkel-Kontorova model

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Dynamical aspects of statistical mechanics (37A60) Rotation numbers and vectors (37E45)

Related Items (8)

Resonant equilibrium configurations in quasi-periodic media: perturbative expansions ⋮ Calibrated configurations for Frenkel-Kontorova type models in almost periodic environments ⋮ Existence and modulation of uniform sliding states in driven and overdamped particle chains ⋮ The analyticity breakdown for Frenkel-Kontorova models in quasi-periodic media: numerical explorations ⋮ Translation numbers for a class of maps on the dynamical systems arising from quasicrystals in the real line ⋮ On the existence of solutions for the Frenkel-Kontorova models on quasi-crystals ⋮ Critical states of strongly interacting many-particle systems on a circle ⋮ Equilibrium configurations for generalized Frenkel-Kontorova models on quasicrystals

Cites Work

• The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
• Spaces of tilings, finite telescopic approximations and gap-labeling
• Space tilings and local isomorphism
• Aubry-Mather theory for functions on lattices
• Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
• On the dynamics of \mathbb{G} -solenoids. Applications to Delone sets
• Repetitive Delone sets and quasicrystals
• ORDERED BRATTELI DIAGRAMS, DIMENSION GROUPS AND TOPOLOGICAL DYNAMICS
• Tiling spaces are inverse limits
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