This mini-course is meant to introduce classical counterparts of some results about quantum transport in solid state physics.
In Sec. II, we state mathematical findings concerning the classical motion in deterministic or random potentials and in magnetic fields. Section III indicates some relations with quantum dynamics and ends with a conjecture.
In Appendix, we gather concepts in Hamiltonian mechanics on manifolds that are used in the main part.
Missing proofs can be found in the cited references, respectively, in standard texts on classical mechanics, like Arnol’d (1989), Abraham and Marsden (1982), or Knauf (2018).
Apologies: The choices made in this text are very subjective, and innumerous important contributions have not been mentioned. In particular, the part on transport only treats single particles. Concerning interacting particles, I highly recommend the classic book (Spohn, 2012) by Herbert Spohn.
Although quantum mechanics is the adequate theory...