2024/09/15 by A. Ya. Maltsev, Maltsev, A. Ya. · 1 citation
Physics and Astronomy · #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2409.09759
We consider the Novikov problem, namely, the problem of describing the level lines of quasiperiodic functions on the plane, for a special class of potentials that have important applications in the physics of two-dimensional systems. Potentials of this type are given by a superposition of periodic potentials and represent quasiperiodic functions on a plane with four quasiperiods. Here we study an important special case when the periodic potentials have the same rotational symmetry. In the generic case, their superpositions have ``chaotic'' open level lines, which brings them close to random potentials. At the same time, the Novikov problem has interesting features also for ``magic'' rotation angles, which lead to the emergence of periodic superpositions.