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Abstract
ABSTRACT A one dimensional stationary transport model accounting for both quantum effects and smallness of coherence length is presented and analyzed. The physical system extension is an interval [a,b] whose length is of the order of few to several times the coherence length of particles. An arbitrary decomposition of the interval into intervals of lengths comparable to coherence length is chosen. On each interval, the particle density is the superposition of densities of scattering states of the Schrodinger equation. The statistics in the various intervals are solution of a linear system whose coefficients depend on the reflexion and transmission coefficients. This system is shown to have a unique minimal solution. In the limit of very small coherence lengths, a collisionless kinetic equation is obtained.
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