  The constraints on the scaling properties of conserved charge densities in
the vicinity of a zero temperature ($T$), second-order quantum phase transition
are studied. We introduce a generalized Wilson ratio, characterizing the
non-linear response to an external field, $H$, coupling to any conserved
charge, and argue that it is a completely universal function of $H/T$: this is
illustrated by computations on model systems. We also note implications for
transitions where the order parameter is a conserved charge (as in a $T=0$
ferromagnet-paramagnet transition).
