2009/06/09 by Shi-Jian Gu, Junpeng Cao, Shu Chen +1
Physics and Astronomy · #Bethe ansatz #Boson #Cold Atom Physics and Bose-Einstein Condensates #Fermion #Ground state #Isospin #Mathematical physics #Particle physics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum electrodynamics #Quantum mechanics #Quantum, superfluid, helium dynamics #Spin (aerodynamics) #Spinor #Wave function #cond-mat.quant-gas #cond-mat.str-el
paper · pdf · doi:10.1016/j.nuclphysb.2009.06.003
25 pages, 10 figres
openalex publication_date 2009/06/09 · arxiv created 2009/07/25 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions with δ-function interactions are studied. Some new sets of Bethe ansatz equations are obtained by using the graded nest quantum inverse scattering method. Many interesting features appear in the system. For example, the wave function has the SU(2|2) supersymmetry. It is also found that the ground state of the system is partial polarized, where the fermions form a spin singlet state and the bosons are totally polarized. From the solution of Bethe ansatz equations, it is shown that all the momentum, spin and isospin rapidities at the ground state are real if the interactions between the particles are repulsive; while the fermions form two-particle bounded states and the bosons form one large bound state, which means the bosons condensed at the zero momentum point, if the interactions are attractive. The charge, spin and isospin excitations are discussed in detail. The thermodynamic Bethe ansatz equations are also derived and their solutions at some special cases are obtained analytically.