  We study a one-dimensional disordered Bose fluid using bosonization, the
replica method and a nonperturbative functional renormalization-group approach.
The Bose-glass phase is described by a fully attractive strong-disorder fixed
point characterized by a singular disorder correlator whose functional
dependence assumes a cuspy form that is related to the existence of metastable
states. At nonzero momentum scale, quantum tunneling between these metastable
states leads to a rounding of the nonanalyticity in a quantum boundary layer
that encodes the existence of rare superfluid regions responsible for the
$\omega^2$ behavior of the (dissipative) conductivity in the low-frequency
limit. These results can be understood within the "droplet" picture put forward
for the description of glassy (classical) systems.
