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Irreversible processes of one-dimensional quantum perfect Lorentz gas isstudied on the basis of the fundamental laws of physics in terms of the complexspectral analysis associated with the resonance state of the Liouville-vonNeumann operator. A limitation of the usual phenomenological Boltzmann equationis discussed from this dynamical point of view. For a Wigner distributionfunction that spreads over moderately small scale comparative to themean-free-path, we found a shifting motion in space of the distribution thatcannot be described by the hydrodynamic approximation of the kinetic equation.The mechanism of the shifting has two completely different origins: one is dueto different value of the imaginary part of the eigenvalue of the Liouvillianand predominates in moderately small wavenumber associated to the spatialdistribution, while the other is due to the existence of the real part of theeigenvalue associated to a wave propagation and predominates in moderatelylarge wavenumber.

Microscopic Description of Quantum Lorentz Gas by Complex Spectral  Representation of the Liouville-von Neumann Equation: A Limitation of the  Boltzmann Approximation