  We analytically study quantum dissipative dynamics described by the
Caldirola-Kanai model with inter-particle interactions. We have found that the
dissipative quantum dynamics of the Caldirola-Kanai model can be exactly mapped
to a dissipationless quantum dynamics under a negative external harmonic
potential, even when the particles are strongly interacting. In particular, we
show that the mapping is valid for the unitary Fermi gas, which is relevant for
cold atoms and nuclear matters.
