Existence and measure of ergodic leaves in Novikov's problem on the semiclassical motion of an electron

Abstract

We show that ``ergodic regime'' appears for generic dispersion relations in the semiclassical motion of electrons in a metal and we prove that, in the fixed energy picture, the measure of the set of such directions is zero.

arXiv comment3 pages

References in corpus (1)

• Topological Phenomena in Normal Metals

Cited by in corpus (8)

• 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
• The second boundaries of Stability Zones and the angular diagrams of conductivity for metals having complicated Fermi surfaces
• Characterization of the set of "ergodic directions" in the Novikov's problem of quasi-electrons orbits in normal metals
• The complexity classes of angular diagrams of the metal conductivity in strong magnetic fields
• Features of the motion of ultracold atoms in quasiperiodic potentials
• The theory of closed 1-forms, levels of quasiperiodic functions and transport phenomena in electron systems
• Numerical analysis of the Novikov problem of a normal metal in a strong magnetic field