Critical point of the two-dimensional Bose gas: an S-matrix approach

A new treatment of the critical point of the two-dimensional interacting Bose gas is presented. In the lowest order approximation we obtain the critical temperature T_c ~ 2 \pi n/[ m \log (2\pi/mg)], where n is the density, m the mass, and g the coupling. This result is based on a new formulation of interacting gases at finite density and temperature which is reminiscent of the thermodynamic Bethe ansatz in one dimension. In this formalism, the basic thermodynamic quantities are expressed in terms of a pseudo-energy. Consistent resummation of 2-body scattering leads to an integral equation for the pseudo-energy with a kernel based on the logarithm of the exact 2-body S-matrix.

💡 Research Summary

The paper introduces a novel theoretical framework for determining the critical point of a two‑dimensional interacting Bose gas. Drawing inspiration from the thermodynamic Bethe ansatz (TBA) used in one‑dimensional integrable models, the authors formulate the finite‑temperature, finite‑density problem in terms of a pseudo‑energy (\varepsilon(p)). This pseudo‑energy governs the Bose occupation number (f(p)=1/