Interacting Many-Body Systems

Xin Zhang, Zi-Fa Yu, Ju-Kui Xue

We theoretically and numerically investigate the coherence of disordered bosonic gas with effective two- and three-body interactions within a two-site Bose–Hubbard model. By properly adjusting the two- and three-body interactions and the disorder, the coherence of the system exhibits new and interesting phenomena, including the resonance character of coherence against the disorder in the purely two- or three-body interactions system. More interestingly, the disorder and three-body interactions together can suppress the coherence of the purely three-body interactions system, which is different from the case in which the disorder and two-body interactions together can enhance the coherence in certain values of two-body interaction. Furthermore, when two- or three-body interactions are attractive or repulsive, the phase coherence exhibits completely different phenomena. In particular, if two- or three-body interactions are attractive, the coherence of the system can be significantly enhanced in certain regions. Correspondingly, the phase coherence of the system is strongly related to the effective interaction energy. The results provide a possible way for studying the coherence of bosonic gas with multi-atoms' interactions in the presence of the disorder.

M. Kira, S. W. Koch

Lorenzo Contessi, Johannes Kirscher, Manuel Pavón Valderrama

We consider few-body systems in which only a certain subset of the particle-particle interactions is resonant. We characterize each subset by a {\it unitary graph} in which the vertices represent distinguishable particles and the edges resonant 2-body interactions. Few-body systems whose unitary graph is connected will collapse unless a repulsive 3-body interaction is included. We find two categories of graphs, distinguished by the kind of 3-body repulsion necessary to stabilize the associated system. Each category is characterized by whether the graph contains a loop or not: for tree-like graphs (graphs containing a loop) the 3-body force renormalizing them is the same as in the 3-body system with two (three) resonant interactions. We show numerically that this conjecture is correct for the 4-body case as well as for a few 5-body configurations. We explain this result in the 4-body sector qualitatively by imposing Bethe-Peierls boundary conditions on the pertinent Faddeev-Yakubovsky~decomposition of the wave function.

Luca Salasnich

Lorenzo Contessi, Johannes Kirscher, Manuel Pavón Valderrama

We consider few-body systems in which only a certain subset of the particle-particle interactions is resonant. We characterize each subset by a unitary graph in which the vertices represent distinguishable particles and the edges resonant two-body interactions. Few-body systems whose unitary graph is connected will collapse unless a repulsive three-body interaction is included. We find two categories of graphs, distinguished by the kind of three-body repulsion necessary to stabilize the associated system. Each category is characterized by whether the graph contains a loop or not: for tree-like graphs (graphs containing a loop) the three-body force renormalizing them is the same as in the three-body system with two (three) resonant interactions. We show numerically that this conjecture is correct for the four-body case as well as for a few five-body configurations. We explain this result in the four-body sector qualitatively by imposing Bethe-Peierls boundary conditions on the pertinent Faddeev-Yakubovsky decomposition of the wave function.