The theory of closed 1-forms, levels of quasiperiodic functions and transport phenomena in electron systems

DOI10.1134/S0081543818060147zbMath1431.82037arXiv1805.05210OpenAlexW2962739336MaRDI QIDQ2280447

S. P. Novikov, Andrei Ya. Maltsev

Publication date: 18 December 2019

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.05210

zbMATH Keywords

magnetic fieldsFermi surfaceelectron systemstransport phenomena in metals

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Transport processes in time-dependent statistical mechanics (82C70) Statistical mechanics of metals (82D35) General geometric structures on low-dimensional manifolds (57M50) Motion of charged particles (78A35) Foliations in differential topology; geometric theory (57R30) Statistical mechanics of magnetic materials (82D40)

Related Items (2)

Topological integrability, classical and quantum chaos, and the theory of dynamical systems in the physics of condensed matter ⋮ Open level lines of a superposition of periodic potentials on a plane

Cites Work

• Diffusion for chaotic plane sections of 3-periodic surfaces
• Interval identification systems and plane sections of 3-periodic surfaces
• Symmetric interval identification systems of order three
• Dynamical systems, topology, and conductivity in normal metals
• Geometry of plane sections of the infinite regular skew polyhedron \(\{4, 6 | 4\}\)
• Proof of S. P. Novikov's conjecture on the semiclassical motion of an electron
• Quasiperiodic functions and dynamical systems in quantum solid state physics
• Finite Gauss measure on the space of interval exchange transformations. Lyapunov exponents
• On connectedness of chaotic sections of some 3-periodic surfaces
• A survey on quasiperiodic topology
• Symmetric band complexes of thin type and chaotic sections which are not quite chaotic
• On the Hausdorff dimension of the Rauzy gasket
• Topology of Plane Sections of Periodic Polyhedra with an Application to the Truncated Octahedron
• The Hamiltonian formalism and a many-valued analogue of Morse theory
• A problem of Novikov on the semiclassical motion of an electron in a uniform almost rational magnetic field
• Deviation for interval exchange transformations
• Levels of quasiperiodic functions on a plane, and Hamiltonian systems
• Proof of S.P. Novikov's conjecture for the case of small perturbations of rational magnetic fields
• The geometry of stability regions in Novikov's problem on the semiclassical motion of an electron
• Characterization of the set of “ergodic directions” in Novikov's problem of quasi-electron orbits in normal metals
• Quasiperiodic functions theory and the superlattice potentials for a two-dimensional electron gas
• An example of a fractal set of plane directions having chaotic intersections with a fixed 3-periodic surface
• Topology of quasi-periodic functions on the plane
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