Year: 2010
Type: article
Abstract: We conduct a rigorous investigation into the thermodynamic instability of an ideal Bose gas confined in a cubic box, without assuming a thermodynamic limit or a continuous approximation. Based on the exact expression of the canonical partition function, we perform numerical computations up to ${10}^{6}$ particles. 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 the Dirichlet boundary condition reveals a thermodynamic instability. Accordingly, we demonstrate that a system consisting of a finite number of particles can exhibit a discontinuous phase transition that features a genuine mathematical singularity, provided we keep not volume but pressure constant. The specific number, $7616,$ can be regarded as a characteristic number of a ``cube,'' which is the geometric shape of the box.
Source: Physical Review A
Authors: Jeong-Hyuck Park, Sang-Woo Kim
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,675
Award: G8511173711
OpenAlex ID: W1985287597