We consider the three-body problem in a generic multiband lattice, and analyze dispersion of trimer states that are made two spin-$\uparrow$ fermions spin-$\downarrow$ fermion due to an onsite attraction between. Based on variational approach, we first obtain exact solution form set coupled integral equations, then reduce it eigenvalue problem. As illustration apply our theory sawtooth numerica...

Many binary systems of interest for gravitational-wave astronomy are orbited by a third distant body, which can considerably alter their relativistic dynamics. Precision computations needed to understand the interplay between corrections and three-body interactions. We use an effective field theory approach derive action describing long time-scale dynamics hierarchical up 1PN quadrupole order. ...