Contributions to the Statistical Mechanics of the One Dimensional Delta-Function Interaction Model.

E. T. Y. Hsieh

Xi-Wen Guan, Feng He

In the 60s Professor Chen Ping Yang with Professor Chen Ning Yang published several seminal papers on the study of Bethe’s hypothesis for various problems of physics. The works on the lattice gas model, critical behavior in liquid–gas transition, the one-dimensional (1D) Heisenberg spin chain, and the thermodynamics of 1D delta-function interacting bosons are significantly important and influential in the fields of mathematical physics and statistical mechanics. In particular, the work on the 1D Heisenberg spin chain led to subsequent developments in many problems using Bethe’s hypothesis. The method which Yang and Yang proposed to treat the thermodynamics of the 1D system of bosons with a delta-function interaction leads to significant applications in a wide range of problems in quantum statistical mechanics. The Yang and Yang thermodynamics has found beautiful experimental verifications in recent years.

S. M. Bortsaǐkin, Yu. V. Mikhaǐlova

Miki Wadati, Go Kato

Statistical mechanics of a one-dimensional system of bosons with repulsive delta-function interaction is studied. Explicit calculations of the partition function and the cluster integrals are carried out. The results coincide with those by the thermal Bethe ansatz (TBA) method. Thermodynamic quantities such as the pressure, the chemical potential and the energy are given both for large and small coupling limits.

Ya. G. Sinaǐ

T. H. Hansson, Jon Magne Leinaas, S. Viefers

We study the statistical mechanics of a two-dimensional Bose gas with a repulsive delta-function interaction, using a mean-field approximation. By a direct counting of states we establish that this model obeys exclusion statistics and is equivalent to an ideal exclusion-statistics gas. We also show that this result is consistent with a full quantum-mechanical treatment of a quasi-two-dimensional system.