Yang-Yang equilibrium statistical mechanics: a brilliant method (Q2821148)

Starting from the Yang-Yang fundamental proposal [\textit{C. N. Yang} and \textit{C. P. Yang}, J. Math. Phys. 10, 1115--1122 (1969; Zbl 0987.82503); \textit{C. N. Yang}, Phys. Rev. Lett. 19, 1312--1315 (1967; Zbl 0152.46301)] which offered a rigorous approach to the thermodynamics of one-dimensional system of bosons, the Yang-Yang equilibrium statistical mechanics is presented here to show that this is capable to meet the thermodynamics of the Lieb-Liniger model [\textit{E. H. Lieb} and \textit{W. Liniger}, Phys. Rev., II. Ser. 130, 1605--1616 (1963; Zbl 0138.23001)] on the whole temperature range. The Bethe ansatz (BA) [\textit{H. Bethe}, Z. Phys. 71, 205--226 (1931; Zbl 0002.37205)] is also treated for the particular form of the wave function to obtain the energy spectrum on the 1D Heisenberg chain, which can be obtained exactly in terms of the BA equation for the models, and on this way the physical properties can be derived using mathematical analysis methods. A wide range of problems may be treated on these lines. A step by step method is shown to help calculations of the thermodynamics of the 1D Bose gas. Ways to introduce the model to the fermions are indicated. Comparison shows the result of the computations of the case of weak and strong interaction.NEWLINENEWLINEFor the entire collection see [Zbl 1348.81032].