  Irreversible processes of one-dimensional quantum perfect Lorentz gas is
studied on the basis of the fundamental laws of physics in terms of the complex
spectral analysis associated with the resonance state of the Liouville-von
Neumann operator. A limitation of the usual phenomenological Boltzmann equation
is discussed from this dynamical point of view. For a Wigner distribution
function that spreads over moderately small scale comparative to the
mean-free-path, we found a shifting motion in space of the distribution that
cannot be described by the hydrodynamic approximation of the kinetic equation.
The mechanism of the shifting has two completely different origins: one is due
to different value of the imaginary part of the eigenvalue of the Liouvillian
and predominates in moderately small wavenumber associated to the spatial
distribution, while the other is due to the existence of the real part of the
eigenvalue associated to a wave propagation and predominates in moderately
large wavenumber.
