Minimal foliations for the high-dimensional Frenkel-Kontorova model
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Publication:2681413
DOI10.1007/S10473-023-0207-3OpenAlexW4310267081MaRDI QIDQ2681413
Xue-Qing Miao, Jian-Hua Ge, Ya-Nan Wang, Wen-Xin Qin
Publication date: 3 February 2023
Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10473-023-0207-3
Interacting particle systems in time-dependent statistical mechanics (82C22) Lattice dynamics; integrable lattice equations (37K60) Monotone flows as dynamical systems (37C65)
Cites Work
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- The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
- Percival Lagrangian approach to the Aubry-Mather theory
- Ghost circles in lattice Aubry-Mather theory
- Secondary invariants of Birkhoff minimizers and heteroclinic orbits
- A criterion for the non-existence of invariant circles
- Minimal solutions of variational problems on a torus
- On minimal laminations of the torus
- Phase-locking in the multidimensional Frenkel-Kontorova model
- A new proof of the Aubry-Mather's theorem
- Aubry-Mather theory for functions on lattices
- Continuity of depinning force
- Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
- Metric properties of minimal solutions of discrete periodical variational problems
- Gradient dynamics of tilted Frenkel-Kontorova models
- Invariant circles and depinning transition
- A dichotomy theorem for minimizers of monotone recurrence relations
- Continuity of the Peierls barrier and robustness of laminations
- On the destruction of minimal foliations
- The laminations of a crystal near an anti-continuum limit
- Ground states and critical points for generalized Frenkel–Kontorova models in \pmb{\mathbb Z}^d
- Ground states and critical points for Aubry-Mather theory in Statistical mechanics
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