  Thin films of Amorphous indium oxide undergo a magnetic field driven
superconducting to insulator quantum phase transition. In the insulating phase,
the current-voltage characteristics show large current discontinuities due to
overheating of electrons. We show that the onset voltage for the
discontinuities vanishes as we approach the quantum critical point.
  As a result the insulating phase becomes unstable with respect to any applied
voltage making it, at least experimentally, immeasurable.
  We emphasize that unlike previous reports of the absence of linear response
near quantum phase transitions, in our system, the departure from equilibrium
is discontinuous. Because the conditions for these discontinuities are
satisfied in most insulators at low temperatures, and due to the decay of all
characteristic energy scales near quantum phase transitions, we believe that
this instability is general and should occur in various systems while
approaching their quantum critical point. Accounting for this instability is
crucial for determining the critical behavior of systems near the transition.
