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Uspekhi Mat. Nauk, 2019, Volume 74, Issue 1(445), Pages 149–184 (Mi umn9859)  

This article is cited in 1 scientific paper (total in 1 paper)

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

A. Ya. Maltseva, S. P. Novikovb

a Landau Institute for Theoretical Physics of Russian Academy of Sciences, Moscow
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: 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.
Bibliography: 56 titles.

Keywords: topological phenomena, Hamiltonian systems, transport phenomena.

DOI: https://doi.org/10.4213/rm9859

Full text: PDF file (843 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2019, 74:1, 141–173

Bibliographic databases:

UDC: 517.938.5
MSC: Primary 37N20, 37E99; Secondary 82C70, 82D35
Received: 22.10.2018

Citation: A. Ya. Maltsev, S. P. Novikov, “Topological integrability, classical and quantum chaos, and the theory of dynamical systems in the physics of condensed matter”, Uspekhi Mat. Nauk, 74:1(445) (2019), 149–184; Russian Math. Surveys, 74:1 (2019), 141–173

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Choudhury S., Mukherjee A., “A Bound on Quantum Chaos From Random Matrix Theory With Gaussian Unitary Ensemble”, J. High Energy Phys., 2019, no. 5, 149  crossref  isi
  • Успехи математических наук Russian Mathematical Surveys
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