Pinning of slidding collective charge state in a 1D attractive fermion   system
  We investigate an interacting fermion model with boundary potential by using Bethe ansatz method. The ground state properties of the system and the boundary effect are discussed. It is found that attractive boundary potential leads to the boundary bound state. An interesting phenomenon is that the slidding collective charges in a periodic system, which is formed due to the attractive interaction among the fermions, will be pinned around the boundary, as long as the negative boundary potential is strong enough. 
Shu Chen, Yupeng Wang, Fan Yang, Fu-Cho Pu