The theory of closed 1-forms, levels of quasiperiodic functions and transport phenomena in electron systems

Abstract

The paper is devoted to the applications of the theory of dynamical systems to the theory of transport phenomena in metals in the presence of strong magnetic fields. More precisely, we consider the connection between the geometry of the trajectories of dynamical systems, arising at the Fermi surface in the presence of an external magnetic field, and the behavior of the conductivity tensor in a metal in the limit ${\omega }_B\tau \to \infty$. The paper contains a description of the history of the question and the investigation of special features of such behavior in the case of the appearance of trajectories of the most complex type on the Fermi surface of a metal.

23 pages, 6 figures, latex

References in corpus (2)

• On the analytical properties of the magneto-conductivity in the case of presence of stable open electron trajectories on a complex Fermi surface
• Oscillation phenomena and experimental determination of exact mathematical Stability Zones for magneto-conductivity in metals having complicated Fermi surfaces

Cited by in corpus (1)

• Quasiperiodic functions on the plane and electron transport phenomena