Quasiperiodic functions and Dynamical Systems in Quantum Solid State Physics

TL;DR

This survey explores the topological aspects of quasiperiodic functions and dynamical systems on Fermi surfaces in quantum solid state physics, building on the Geometric Strong Magnetic Field Limit theory.

Contribution

It develops new topological insights into quasiperiodic functions within the context of dynamical systems on Fermi surfaces, extending previous physical theories.

Findings

New topological properties of quasiperiodic functions identified

Enhanced understanding of dynamical systems in quantum materials

Connections established with the Geometric Strong Magnetic Field Limit

Abstract

This is a survey article dedicated to the study of topological quantities in theory of normal metals discovered in the works of the authors during the last years. Our results are based on the theory of dynamical systems on Fermi surfaces. The physical foundations of this theory (the so-called "Geometric Strong Magnetic Field Limit") were found by the school of I.M.Lifshitz many years ago. Here the new aspects in the topology of quasiperiodic functions are developed.