The Thermodynamics and Fractional Statistics of the Spinor Bose Gas

Abstract

We present a comprehensive analysis of the exact Bethe ansatz solution for the onedimensional spinor Bose gas. The Bethe ansatz equations and the thermodynamic Bethe ansatz equations are derived, before investigating properties of these equations in limiting regimes. We explore the difference between spinless and spinor particles in the onedimensional Bose gas. For the spinor Bose gas, we present a new approximation to the thermodynamic Bethe ansatz equations which allows them to be solved in the strong coupling regime. We derive the first order correction to the solutions of the thermodynamic Bethe ansatz equations in a low temperature regime, where spin effects are most evident. We then derive thermodynamic quantities for this model, adding a first order correction to the thermodynamics of the spinless system. The subject of fractional exclusion statistics is presented, and its significance with regards to the spinless Bose gas is discussed. We also discuss its significance with regards to the spinor Bose gas, and find a regime in which non-mutual statistics may be applied to the spinor Bose gas to obtain expansions of thermodynamic quantities. These expressions are seen to improve upon previous analytical results for the model.