Topological integrability, classical and quantum chaos, and the theory of dynamical systems in the physics of condensed matter

@article{Maltsev2019TopologicalIC,
  title={Topological integrability, classical and quantum chaos, and the theory of dynamical systems in the physics of condensed matter},
  author={A. Ya. Maltsev and Sergei Novikov},
  journal={Russian Mathematical Surveys},
  year={2019},
  volume={74},
  pages={141 - 173}
}
This survey is devoted to questions connected with the Novikov problem of describing the geometry of level curves of quasi-periodic functions on the plane with different numbers of quasi-periods. Considered here are the history of the question, the current state of research in this field, and a number of applications of this problem to various physical problems. The main focus is on applications of results obtained in this area to the theory of transport phenomena in electron systems… 
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5 Citations

Distinctive Features of Oscillatory Phenomena in Reconstructions of the Topological Structure of Electron Trajectories on Complex Fermi Surfaces
  • A. Maltsev
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    Journal of Experimental and Theoretical Physics
  • 2021
We consider the behavior of classical and quantum oscillations in metals with complex Fermi surfaces near the directions of $\, {\bf B} \, $ corresponding to changes in the topological structure of…
Reconstructions of the Electron Dynamics in Magnetic Field and the Geometry of Complex Fermi Surfaces
The paper considers the semiclassical dynamics of electrons on complex Fermi surfaces in the presence of strong magnetic fields. The reconstructions of the general topological structure of such…
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A bstractIn this article, using the principles of Random Matrix Theory (RMT) with Gaussian Unitary Ensemble (GUE), we give a measure of quantum chaos by quantifying Spectral From Factor (SFF)…
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The Arnoux-Rauzy systems are defined in [5], both as symbolic systems on three letters and exchanges of six intervals on the circle. In connection with a conjecture of S.P. Novikov, we investigate…

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