Chaotic Trajectories on Fermi Surfaces and Nontrivial Modes of Behavior of Magnetic Conductivity

We present here a survey of questions related to recently discovered types of non-closed electron trajectories on complex Fermi surfaces, corresponding to chaotic dynamics in the quasi-momentum space. Trajectories of this type have been found and are currently quite well studied theoretically. However, their experimental detection is still to be done. Here we discuss the geometric properties of such trajectories, the likelihood of their occurrence on real Fermi surfaces, and the behavior of the magnetoconductivity in the limit ω B τ → ∞ when they occur. The review includes the latest results of research on chaotic trajectories for dispersion relations of the most general form.