Quasiperiodic functions on the plane and electron transport phenomena

Abstract

While quasiperiodic functions in one variable appeared in applications since Eighteen hundreds, for example in connection with the trajectories of mechanical systems with 2n degress of freedom having n commuting first integrals, the first applications of multivariable quasiperiodic functions were found only in Seventies, in connection with solitonic solutions of the KdV equation. Later, several other physical applications were found, especially in connection with Solid State Physics, in particular with the electron transport phenomena. In this article we reformulate, specifically in terms of the topology of level sets of quasiperiodic functions on the plane, some fundamental theoretical results found in Eighties and Nineties, then we review the physical models of electron transport and their connections with quasiperiodic functions and finally we present some old and new numerical results on the level sets of some specific family of quasiperiodic functions, some of which related to the magnetoresistance in normal metals.