  In this article we develop an exact(non-adiabatic,non-perturbative) density
matrix scattering theory for a two component quantum liquid which interacts or
scatters off from a generic spin-dependent quantum potential. We find that the
number or charge density in scattered fluid,$\text{Tr}({\varrho}_{sc})$ depends
on {non-trivial quantum interference coefficients},
${\cal{Q}}^{\alpha\beta}_{0ijk}$ which arises due to quantum interference
between spin-independent and spin-dependent scattering amplitudes and among
spin-dependent scattering amplitudes. The effect of quantum interference
coefficients can be include by defining a {\bf vector order parameter}
$\bm{Q}$. We find that in presence of spin-dependent interaction the {\bf
vector order parameter} $\bm{Q}$ is necessarily non-zero and is related to the
commutator and anti-commutator of scattering matrix $\cal{S}$ with its dagger
$\cal{S}^{\dagger}$. It is further shown that $\bm{Q}\neq 0$, implies four
physically equivalent conditions,i.e, {\bf spin-orbital entanglement is
non-zero}, {\bf Non-Abelian scattering phase,i.e, matrices}, scattering matrix
is {\bf Non-Unitary} and the broken time reversal symmetry for scattered
density matrix. This also implies that quasi particle excitation are anyonic in
nature, hence, charge fractionalization is a natural consequence. This aspect
has also been discussed from the perspective of number or charge density
conservation, which implies i.e,
$\text{Tr}({\varrho}_{sc})=\text{Tr}({\varrho}_{in})$. On the other hand
$\bm{Q}=0$ turns out to be a mathematically forced unphysical solution in
presence of spin-dependent potential or scattering which is equivalent to {\bf
Abelian} hydrodynamics ,{\bf Unitary} scattering matrix, absence of spin-space
entanglement, and preserved time reversal symmetry.
