Ideal Bose Gas revisited: How Many Is Different?

Jeong-Hyuck Park (Sogang Univ.)

In comparison to classical mechanics, crucial features of quantum mechanics are that, elementary particles in Nature are identical and physical quantities do not assume continuous values. In this talk, we revisit the ideal Bose gas confined in a cubic box as a simplest quantum system. Powered by a modern supercomputer, without assuming any continuous approximation, we investigate into the equation of the state of the ideal Bose gas. We report that if the number of particles is equal to or greater than a certain critical value, which turns out to be 7616, the isobar curve on the temperature and volume plane zigzags, revealing a thermodynamic instability. Accordingly we demonstrate - for the first time - that, a system consisting of finite number of particles can exhibit a discontinuous phase transition featuring a genuine mathematical singularity, provided we keep not volume but pressure constant. We also discuss the thermodynamic limit of our finding.