  The skin effect has been discovered in non-Hermitian Hamiltonian systems
where all the eigenstates have their amplitudes concentrating to the open
boundaries of the systems and decaying exponentially into the bulk. Later,
certain open systems obeying the quadratic Lindblad equation has also been
found to exhibit the skin effect, which is manifested in the ``chiral damping"
phenomenon as the particle populations, decaying from their initial uniform
unity values, show asymmetry with respect to the open boundaries. However, in
those open systems, each cell couples to the environment in an identical way.
It is natural to expect that the long time steady state of those open systems
shall have spatially uniform particle populations. Furthermore, particle
population variations due to the excitation of normal modes on top of the
steady state shall also not show asymmetry with respect to the open boundaries.
To reconcile the natural expectations with the skin effect, we employ an
adjoint fermion formalism to study the quadratic Lindbladian systems. We work
out the long time steady state and the normal modes on top of it, which exhibit
no asymmetry as expected. We show that it is the interference between the
normal modes that gives rise to the skin effect.
