On the Novikov problem for superposition of periodic potentials

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Bibliographic Details
Main Author:	Maltsev, A. Ya.
Format:	Preprint
Published:	2024
Subjects:	Mathematical Physics
Online Access:	Acceder al recurso
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author	Maltsev, A. Ya.
author_facet	Maltsev, A. Ya.
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2409_09759
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	On the Novikov problem for superposition of periodic potentials Maltsev, A. Ya. Mathematical Physics 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.
title	On the Novikov problem for superposition of periodic potentials
topic	Mathematical Physics
url	https://arxiv.org/abs/2409.09759

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