  The symmetric and antisymmetric parts of the linear conductivity describe the
dissipative (Ohmic) and nondissipative (Hall) parts of the current. The Hall
current is always transverse to the applied electric field regardless of its
orientation; the Ohmic current is purely longitudinal in cubic crystals, but in
lower-symmetry crystals it has a transverse component whenever the field is not
aligned with a principal axis. In this work, we extend that analysis beyond the
linear regime. We consider all possible ways of partitioning the current at any
order in the electric field without taking symmetry into account, and find that
the Hall vs Ohmic decomposition is the only one that satisfies certain basic
requirements. A general prescription is given for achieving that decomposition,
and the case of the quadratic conductivity is analyzed in detail. By performing
a symmetry analysis we find that in five of the 122 magnetic point groups the
quadratic dc conductivity is purely Ohmic and even under time reversal, a type
of response that is entirely disorder mediated.
