Bethe-ansatz study of the Bose-Fermi mixture (opens in new tab)

We consider a one-dimensional mixture of bosons and spinless fermions with contact interactions. In this system, the excitations at low energies are described by four linearly dispersing modes characterized by two excitation velocities. Here we study the velocities in a system with equal interaction strengths and equal masses of bosons and fermions. The resulting model is integrable and admits an exact Bethe-ansatz solution. We analyze it and analytically derive various exact results, which i...