Dynamical Systems, Topology and Conductivity in Normal Metals

Abstract

New observable integer-valued numbers of the topological origin were revealed by the present authors studying the conductivity theory of single crystal 3D normal metals in the reasonably strong magnetic field ($B \leq 10^{3} Tl$). Our investigation is based on the study of dynamical systems on Fermi surfaces for the motion of semi-classical electron in magnetic field. All possible asymptotic regimes are also found for $B \to \infty$ based on the topological classification of trajectories.