Thermodynamic instability and first-order phase transition in an ideal Bose gas

Details Thermodynamic instability and first-order phase transition in an ideal Bose gas Thermodynamic instability and first-order phase transition in an ideal Bose gas

2008-09-26

arxiv.org/abs/0809.4652v6

Phys. Rev. A 81, 063636 (2010)

Physics

Condensed Matter

Statistical Mechanics

1+21 pages; 3 figures (2 color and 1 B/W); Final version to appear in Physical Review A. Title changed from the previous one,

Scientific paper

10.1103/PhysRevA.81.063636

We conduct a rigorous investigation into the thermodynamic instability of ideal Bose gas confined in a cubic box, without assuming thermodynamic limit nor continuous approximation. Based on the exact expression of canonical partition function, we perform numerical computations up to the number of particles one million. 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 ideal Bose gas subject to Dirichlet boundary condition reveals 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. The specific number, 7616 can be regarded as a characteristic number of 'cube' that is the geometric shape of the box.

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