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Very recent atom-optics experiments addressing the dynamics of a small number of bosons and fermions in one dimension have lead to a renewed interest in theoretical problems concerned with the escape properties of few-particle systems. In particular, particle-particle interactions and quantum statistics have been shown to have a significant influence. In our paper which can be found here, we have extended the theory to account for the influence of boundary conditions and demonstrated that they can be of equal importance. Moreover, in certain cases, boundary conditions may lead to a complete suppression of the escape through the existence of a bound state.
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The animations bellow show a single quantum particle represented as wavepacket diffusing to the right while being reflected off a hard wall at zero. Robin boundary conditions are used at the wall controlled by the parameter $\eta$ which can be interpreted as a phase shift. For $\eta$ negative (right animation), a bound state (i.e. non-diffusive state) exists corresponding to an effective zero-range attractive force causing the wavefunction to "stick" to the wall. As a result the diffusive properties for the two cases are essentially different and can be controlled by the parameter $\eta$. For more details check out our paper (10).
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