Collective Excitations And Stability Analysis Of Homogeneous Two-Component Tonks Gas

In this paper, we first gave a brief introduction to the theoretical models of one-dimensional Bose system, including Lieb-Liniger model and Tonks gas which appears when the parameterγapproaches infinite in Lieb-Liniger model. A modified scheme for Gross-Pitaevskii equation was introduced to describe one-dimensional Bose system. We then summarized the main theoretical and experimental results on excitations of single-component Bose system in literatures. The excitations and stability of two-component Bose system were investigated. To get the excitation spectra of two-component system in Tonks regime, we started from the coupled time-dependent nonlinear equations of two-component Tonks gas and formulated their hydrodynamics and the corresponding fluctuation equations. The excitation spectra in homogeneous case were calculated, which enable us to analyze the stability condition of two-component system in Tonks regime. Compared with that of two-component system in mean-field regime, a very different conclusion was arrived. The stability condition in mean-field regime is related to interaction constant of particles, while that in Tonks regime depends crucially on the ratio of inter-component atomic mass and density.