Non-dissipative   transport coefficients in Quantum Hall Effect are precisely quantized.

These transport coefficients are Chern numbers and for that reason can not be changed continuously.
This fact is intimately related to the  Quillen holomorphic anomaly (a generalization of conformal anomaly)

 in such manner that the transport coefficients are encoded in the  Quillen metric on the determinant line bundle.
The relation seems  general, and applicable to any non-dissipative transport,

 but I will discuss it terms  of Quantum Hall effect, the case study.