Impact of dark states on the stationary properties of quantum particles with off-centered interactions in one dimension

We present a generalization of the two-body contact interaction for non-relativistic particles trapped in one dimension. The particles interact only when they are a distance c apart. The competition of the interaction length scale with the oscillator length leads to three regimes identified from the energy spectra. When c is less than the oscillator length, particles avoid each other, whereas in the opposite case bunching occurs. In the intermediate region where the oscillator length is comparable to c, both exclusion and bunching are manifested. All of these regions are separated by dark states, i.e. bosonic or fermionic states which are not affected by the interactions.