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
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.
topological phenomena, Hamiltonian systems, transport phenomena.
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Russian Mathematical Surveys, 2019, 74:1, 141–173
MSC: Primary 37N20, 37E99; Secondary 82C70, 82D35
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
\by A.~Ya.~Maltsev, S.~P.~Novikov
\paper Topological integrability, classical and quantum chaos, and the theory of dynamical systems in the physics of condensed matter
\jour Uspekhi Mat. Nauk
\jour Russian Math. Surveys
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