  Because a material with an incommensurate charge density wave (ICDW) is only
quasi-periodic, Bloch's theorem does not apply and there is no sharply defined
Fermi surface. We will show that, as a consequence, there are no quantum
oscillations which are truly periodic functions of $1/B$ (where $ B$ is the
magnitude of an applied magnetic field). For a weak ICDW, there exist broad
ranges of $1/B$ in which approximately periodic variations occur, but with
frequencies that vary inexorably in an unending cascade with increasing $1/B$.
For a strong ICDW, e.g. in a quasi-crystal, no quantum oscillations survive at
all. Rational and irrational numbers really are different.
