  We study the nonequilibrium properties of a nonergodic random quantum chain
in which highly excited eigenstates exhibit critical properties usually
associated with quantum critical ground states. The ground state and excited
states of this system belong to different universality classes, characterized
by infinite-randomness quantum critical behavior. Using strong-disorder
renormalization group techniques, we show that the crossover between the zero
and finite energy density regimes is universal. We analytically derive a flow
equation describing the unitary dynamics of this isolated system at finite
energy density from which we obtain universal scaling functions along the
crossover.
