= Dark state of a driven Hamiltonian
{title2=$H_1|D\rangle=0,\quad H_0|D\rangle=E_D|D\rangle$}
Such a <quantum state> remains an <eigenstate> of $H_0+f(t)H_1$ for every <control input>. Its projector commutes with all available generators, so its population is conserved. This obstructs full-space <pure-state controllability> even when the orthogonal bright subspace can be controlled. An instantaneous dark state of a slowly varying <Quantum Hamiltonian> instead supports <adiabatic quantum control> if a <spectral gap> and slowness condition are maintained.
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